Learning Task 1: Write and answer the following in your answer sheet
1. Evaluate the following polynomials in your answer sheet.
f(x) = x4 – 7x2 + 2x - 6
x=1
b. f(x) = 10x3 + 4x2 - 5
x = -3
f(x) = x4 + 5x3 - 2x + 3
a.
at
at
C.
find (2))2
2. Factor each polynomial completely using any method
(x + 1)(x2 – 5x + 6)
b. (x2 - * - 6)(x2 + 6x + 9)
x3 + 3x2 - 4x - 12
a.
C.
LABAR
Answers
Answer:
Evaluating Polynomials:
a. f(1) = -10
b. f(-3) = -239
c. f(2)² = 3125
Factoring Polynomials:
a. (x + 1)(x² - 5x + 6) = (x + 1)(x - 3)(x - 2)
b. (x² - x - 6)(x² + 6x + 9) = (x - 3)(x + 2)(x + 3)(x + 3)
c. x³ + 3x² - 4x - 12 = (x + 3)(x - 2)(x + 2)(x - 2)(x + 2)
A polynomial can be evaluated and factored by long division, factoring and synthetic division methods.
1. Evaluate polynomials
[tex]\mathbf{f(x) = x^4 - 7x^2 + 2x - 6}[/tex]
Substitute 1 for x
[tex]\mathbf{f(1) = 1^4 - 7(1)^2 + 2(1) - 6}[/tex]
[tex]\mathbf{f(1) = 1 - 7 + 2 - 6}[/tex]
[tex]\mathbf{f(1) = -10}[/tex]
[tex]\mathbf{f(x) = 10x^3 + 4x^2 - 5}[/tex]
Substitute -3 for x
[tex]\mathbf{f(-3) = 10(-3)^3 + 4(-3)^2 - 5}[/tex]
[tex]\mathbf{f(-3) = -270 + 36 - 5}[/tex]
[tex]\mathbf{f(-3) = -239}[/tex]
[tex]\mathbf{f(x) =x^4 + 5x^3 - 2x + 3}[/tex]
Substitute 2 for x
[tex]\mathbf{f(2) =2^4 + 5(2)^3 - 2(2) + 3}[/tex]
[tex]\mathbf{f(2) =16 + 40 - 4 + 3}[/tex]
[tex]\mathbf{f(2) =55}[/tex]
Square both sides
[tex]\mathbf{f(2)^2 =3025}[/tex]
Hence, the results of evaluating the polynomials are [tex]\mathbf{f(1) = -10}[/tex], [tex]\mathbf{f(-3) = -239}[/tex] and [tex]\mathbf{f(2)^2 =3025}[/tex]
2. Factor the polynomials
[tex]\mathbf{(x + 1)(x^2 - 5x + 6)}[/tex]
Expand
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x^2 - 2x - 3x + 6) }[/tex]
Factorize
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x(x - 2) - 3(x - 2) )}[/tex]
Factor out x - 2
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex]
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9)}[/tex]
Expand
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x^2 +2x - 3x - 6)(x^2 + 3x +3x + 9)}[/tex]
Factorize
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [x(x +2) - 3(x + 2)][x(x + 3) +3(x + 3)]}[/tex]
Factor out x + 2 and x + 3
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [(x - 3) (x + 2)][(x + 3)(x + 3)]}[/tex]
Remove square brackets
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex]
[tex]\mathbf{x^3 + 3x^2 - 4x - 12}[/tex]
Factorize
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = x^2(x + 3) - 4(x + 3)}[/tex]
Factor out x + 3
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x^2 -4) (x + 3)}[/tex]
Apply the difference of two squares
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]
Hence, the results of factoring the polynomials are [tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex], [tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex] and [tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]
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Related Questions
Look at at pic attached! Pls hurry :( 21 points
Answers
Answer:
C option
Step-by-step explanation:
bcz root of 121 is 11. then 2/3 +11 will give you a rational number.
Answer:
2/7 + square root of 121 (the third one)
Step-by-step explanation:
a rational number is a number where if you write it as a fraction, both the numerator and denominator are integers (numbers like 1 and 2 but not like 3.4 or 5.6)
the equation simplified a bit looks like this:
2/7 + 11/1
anddd so all the numbers are integers which means that expression is correct :3
If a = -4 what is the value of 3a?
Answers
Answer:
3a = -12
hope it helps...
During one year, a family made 3 trips to the museum. The distance from their house to the museum is 47 miles. How many miles did the family drive in 3
Answers
Answer:
282 miles
Step-by-step explanation:
47 x 6 = 282
Answer:
282 miles
Step-by-step explanation:
When the family goes to the museum, its 47 miles. When they come back, its another 47 miles. They did that three times, so multiply by 6.
46 x 6 = 282 miles.
Divide by two if you need just the one-way trip.
A ferris wheel can fit 75 people in 25
minutes. Calculate the unit rate of people
per minute.
Answers
Answer:
3people/minute
Step-by-step explanation:
75/25=3
Computer packages at an electronics store are priced $1,729.99, $2,249.99, $2,139.99, $1,979.99, and $999.99.
What is the range of the prices of the computer packages?
Answers
Answer:1250
Step-by-step explanation:
You take the highest number 2249.99 and subtract the lowest number 999.99 to get the range of 1250
The range of the prices of the computer packages is $1250.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given,
Computer packages at an electronics store are priced $1,729.99, $2,249.99, $2,139.99, $1,979.99, and $999.99.
One thousand seven hundred and twenty nine point nine nine comma two thousands two hundred forty nine point nine nine comma two thousand one hundred thirty nine point nine nine comma one thousand nine hundred seventy nine point nine nine comma nine hundred ninety nine point nine nine.
Range is the difference between highest value minus lowest value.
Range=Highest value - Lowest value
Range=$2,249.99-$999.99.
Range=$1250
Hence, the range of the prices of the computer packages is $1250.
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the size of a rectangular computer screen is determined by the length of its diagonal. tom buys a 52cm screen that is 33 cm high. how Long is the base of the screen?
Answers
Answer:
40.20cm approx
Step-by-step explanation:
Step one
given data
We are told that the dimension of a computer screen
diagonal= 52 cm
height= 33cm
Length = ?
Required
The length of the base of the screen
Step two
Let us use Pythagoras theorem to find the length of the base
Hyp^2= Opp^2+ Adj^2
52^2= 33^2+ L^2
2704= 1089+L^2
L^2= 2704-1089
L^2= 1615
L=√1615
L= 40.20cm approx
The length is 40.20cm approx.
Fill in the table to show a proportional relationship and then identify the constant of proportionality for the cost to the number of yoga classes. In the answer box, please list the constant of proportionality
Answers
Answer:
30 = 2
60 = 4
90 = 6
120 = 8
Step-by-step explanation:
60/4 = 15
15 = 1
30 = 2
45 = 3
60 = 4
75 = 5
90 = 6
105 = 7
120 = 8
can u pls help me with this question asap
Answers
Answer:
.
Step-by-step explanation:
Answer:
0.0025
Step-by-step explanation:
Please help me with this!
Answers
Answer: the answer is d.
HELP PLEASEEEE IM BEGGING YOU
Answers
Answer:
40
3
9
70
6
7
10
2
42
8
Step-by-step explanation:
let's hope i didn't read naything wrong
A bouncy ball is dropped such that the height of its first bounce is 6.5 feet and each
successive bounce is 75% of the previous bounce's height. What would be the height
of the 10th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
Answer:
.3 feet
Step-by-step explanation:
quick math
6.5*75%^10
. Which expression is equivalent to 14-9?
math
Answers
Answer:
5
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
For a charity event, raffle tickets are printed such that they have a vowel (excluding ») as the first character and a
prime number less than 10 as the second digit. (Note that 1 is not a prime number.)
The probability that the winning ticket has the vowel contained in the word event and the digit is the number of
letters in the word event is 1/20 .
Reset
Next
Answers
Answer:
yes 1/20 is correct
Step-by-step explanation:
The probability that the winning ticket will have the letter e on it would be P=5%.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
For the probability of two independent events:
P(A and B) = P(A) P(B)
so we have to find the probability for each event to happen.
For a charity event, raffle tickets are printed such that they have a vowel (excluding ») as the first character and a prime number less than 10 as the second digit.
(Note that 1 is not a prime number.)
There are 5 vowels in the alphabet (a, e, i, o, and u).
Therefore the probability for the first letter to be e
P(A) = 1/5
We also know there are 4 prime numbers between 0 and 10 (2, 3, 5, 7)
so the probability for the number to be a 5 is:
P(B) = 1/4
Now, the probability of getting a ticket that starts with an e and ends with a 5
P(A and B) = P(A) P(B)
= 1/4 x 1/5
= 1/20
Therefore, the probability is 5%.
Learn more about probability here;
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Write this multiplication expression using an exponent: 2 . 2 . 2 = ?
Answers
Answer:2^3
Step-by-step explanation:
What type of arc is AB
Answers
I'm sorry I don't know the answer but I do have to say that you are loved and no matter how many mistakes you make you will still always be loved. Step-by-step explanation:
Answer:
B. A minor arc
Step-by-step explanation:
Trust me bro
PLS HELP!!!
A triangular prism. The rectangular sides are 12 feet by 3 feet, 12 feet by 5 feet, and 12 feet by 4 feet. The 2 triangular sides have a base of 3 feet and height of 4 feet. The area of each triangular base is: A = 1/2(b)(h) A = 1/2(3)(4) A = ft2 There are two bases, so total base area is ft2. The lateral area is: A = (12)(3) + 12(5) + 12(4) A = ft2 The total surface area is ft2.
Answers
Answer:
The lateral area is 144 ft^2
The Total surface area is 156ft^2
Step-by-step explanation:
:)
Answer:
6, 12, 144, 156
Step-by-step explanation:
The area of each triangular base is: A = 1/2(b)(h) A = 1/2(3)(4) A = 6 ft2
There are two bases, so total base area is 12 ft2.
The lateral area is: A = (12)(3) + 12(5) + 12(4) A = 144 ft2
The total surface area is 156 ft2.
I think this is right but want to check need help 25 points!!!
Answers
Answer:yes your Most definitely correct
Step-by-step explanation:
Express the quotient in simplest form.
x
x² - 4 ² x² - 6x
x3 +7x2 * x2 + 4x-21
Answers
Answer:
Try the examples below.
2 x ^− 2 x
x− 2/ x + 4 ≥ 0
9 /x + 8 − 2/ x + 7
Step-by-step explanation:
Im kinda confused tho how its set up but i still tried tho.
Determine whether a triangle with the given side lengths is a right triangle. Side lengths: 10, 11, 15 5, 12, 13 12, 15, 20 16, 30, 34
Answers
Answer:
Step-by-step explanation: Use the Pythagorean Theorem to check this.
Remember that the squares of the lengths of the two smaller sides should be equal to the square of the bigger side.
10,11,15 = NO
5,12,13 = YES
12,15,20 = NO
16,30,34= YES
Hope this helps.
need some help with this problem, cant really figure out how to do this
Answers
Answer:
[tex] -2.5f + 0.3f - 16 - 9 = -2.2f - 25 [/tex]
Step-by-step explanation:
Given:
[tex] -2.5f + 0.3f - 16 - 9 [/tex]
Required:
Simplify
SOLUTION:
[tex] -2.5f + 0.3f - 16 - 9 [/tex]
Add like terms together
-2.5f and 0.3f are like terms. If you add them together you'd get -2.5f + 0.3f = -2.2f
-16 and -9 are like terms. Adding toghter, you'd get -16 +(-9) = -25
So we would have:
[tex] -2.2f - 25 [/tex]
Identify whether the following items best fit with a discrete or a continuous model. Then determine whether it is a linear (arithmetic) or exponential (geometric) relationship that is being described. Finally, write the function that represents the situation.
One square inch is infected by bacteria. For every hour that passes the amount of area infected by the bacteria doubles.
Answers
Answer:
it will be a continuous model
Step-by-step explanation:
weekend weekend assume every amount of area infected by the bed period doubles as hour passes
Can someone please help me on this? I've been trying for hours and can't seem to find the answer.
Answers
Answer: The area of the shape is 90 ft.
Step-by-step explanation:
Draw a line so the shape looks like a triangle and small rectangle.
First, we have to find the area of the rectangle.
Area of rectangle: length x width
The rectangle has a length of 6 ft and a width of 3 ft.
Area of rectangle: 6 x 3 = 18 ft
Now to find the area of the triangle.
Area of triangle: 1/2 x base x height
The triangle's base: 15 - 3 = 12
The triangle's height: 6 + 6 = 12
Area of the triangle: 1/2 x 12 x 12
= 1/2 x 144 = 72ft
To find the area of the entire shape you have to add the area of the rectangle and triangle together.
Area of shape = Area of rectangle + Area of triangle
A of shape = 18 ft + 72 ft
The area of the shape is 90 ft.
Hope that helped!
Figure A is a scale image of Figure B. 6 12 Figure A 9 x Figure B What is the value of x?
Answers
Answer:
18
Step-by-step explanation:
6 is twice less than 12
X=9*2=18
1.4(X + 3) *
[
4x + 3
X + 12
4x + 12
Answers
Answer:
4x + 12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Step-by-step explanation:
Step 1: Define
4(x + 3)
Step 2: Expand
Distribute 4: 4(x) + 4(3)Multiply: 4x + 12Answer:
[tex] \huge4(x + 3) = 4x + 12[/tex]
4x+12 is the right answer.WILL GIVE BRAINLY What is 5x = 25??
Answers
Answer: x=5 bc 5 times 5 is 25
Ste-by-step explanation:
25/5=5
The answer is X=5
I NEED TO GET THIS DONE BEFORE THE 8TH
I forgot how to do this can I get some help.
Answers
Answer:
Step-by-step explanation:
they want to know the high and low quiz scores... that's all
At 8:00 Aam the temperture is 53 at 11:00 Am it is 69
Answers
Answer:
what is the question?
Step-by-step explanation:
all u have is the numbers
Game Stop is selling a video game for 15% off $35.
Answers
Answer:
School related questions please
Step-by-step explanation:
And thanks for telling me
$40.00 x 0.35 =$14.00
$40.00 - $14.00 = $26.00
The since the game is 35% off so the game that costed $40.00 now costs $26.00 right after the discount
4x−5 for x=10
Please, I really need the answer.
Answers
Answer:
4(10)-5=35
Step-by-step explanation:
4(10)=40-5=35
4(10) is the same as 4x10
So think about it like 4x10-5
I hope this helps ;}
What is the difference of 30 and -12?
Answers
the difference between 30 and -12 is 42
30 + 12 = 42
