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

Learning Task 1: Write And Answer The Following In Your Answer Sheet1. Evaluate The Following Polynomials

Answers

Answer 1

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)  

Answer 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]

Read more about polynomials at:

https://brainly.com/question/11536910


Related Questions

Convert the mixed number below to an improper fraction.

523

Answers

Answer:

17/3

Step-by-step explanation:

if you meant 5 2/3

Multiply the denominator by the whole number

3 x 5= 15

Add the answer above to the numerator

15 + 2= 17

Write the answer from above over the denominator

17/3

!Please help!

Antoine is drawing a scale map of the park he uses a scale of 1cm : 15 paces. A pond is 75 paces from the front gate of the park how far is the pond from the gate on the map

Answers

Answer:

5

Step-by-step explanation:

i just did it

1 hours 20 min : 2 hours ratio

Answers

1:20 i think sooo.Je suis américain et habite dans les montagnes vertes du vermont . Je premier apprend français il y a un an parce que c'est un beau langue . Oui, je sais mon français est mauvais, mais J'aime l'apprendre . Je suis dix-sept et j'ai un chien blanc petit . Ma famille l'appelle snowball et il est tres gentil . Mon préféré endroit en la monde est les montagnes car ils sont très beau dans tout quatre saisons . Merci pour votre temps et au revoir .

The angle measurements in the diagram are represented by the following expressions.
B
А
Solve for x and then find the measure of

Answers

Answer:

[tex]x = 20^{\circ}[/tex]

[tex]\angle A = 150^{\circ}[/tex]

Step-by-step explanation:

Given

[tex]\angle A = 8x - 10[/tex]

[tex]\angle B = 3x + 90[/tex]

See attachment

From the attachment A and B are vertically opposite.

This implies that:

[tex]\angle A = \angle B[/tex]

Substitute values for A and B

[tex]8x - 10 = 3x + 90[/tex]

Collect Like Terms

[tex]8x - 3x = 10 + 90[/tex]

[tex]5x = 100[/tex]

Solve for x

[tex]x = \frac{100}{5}[/tex]

[tex]x = 20^{\circ}[/tex]

Substitute 20 for x in [tex]\angle A = 8x - 10[/tex]

[tex]\angle A = 8 * 20 - 10[/tex]

[tex]\angle A = 150^{\circ}[/tex]

Calculate the correlation coefficient, r, for the data below.

Answers

This question is incomplete, the complete question is;

Calculate the correlation coefficient, r, for the data below.

X = -10  -8  -1  -4  -6  -7  -5  -3  -2  -9

Y = -15  -13  4  -4  -7  -11  -6  -2  1  -13

Answer: the correlation coefficient, r, for the data is 0.9896

Step-by-step explanation:

Given the data in the question;

correlation coefficient r = ?

we know that, C_Coeff is;

r = [ (Zn(∑xy) - (∑x)(∑y) ] / [ √[( n∑x² - (∑x)²) ( n∑y² - (∑y)²)] ]

so ;

       X        Y        X²        Y²        XY

     -10     -15       100      225      150

     -8      -13        64       169       104

     -1         4          1        16           -4

     -4       -4         16       16           16

     -6       -7         36      49          42

     -7       -11         49      121         77

     -5       -6         25      36         30

     -3       -2          9         4            6

     -2       1            4         1            -2

     -9      -13         81       169         117

∑   -55     -66      385     806        536

now we substitute our values into the formula

r = [ (10×536 - (-55)(-66) ] / [ √[( 10×385 - (-55)²) ( 10×806 - (-66)²)] ]

r = 1730 / √( 825 × 3704 )

r = 1730 / √3055800

r = 1730 / 1748.0846

r = 0.9896

Therefore the correlation coefficient, r, for the data is 0.9896

What is 42= -7 × (z - 3)?

Answers

Answer:

z=-3

Step-by-step explanation:

Answer:

z=3

Step-by-step explanation:

42=−7(z−3)

Simplify both sides of the equation.

42=−7(z−3)

42=(−7)(z)+(−7)(−3)(Distribute)

42=−7z+21

Flip the equation.

−7z+21=42

Subtract 21 from both sides.

−7z+21−21=42−21

−7z=21

Divide both sides by -7.

-7z/-7=21/7

z=3

what is the quotient? can someone please help.

Answers

Answer:

-3

Step-by-step explanation:

hope this helps

How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings if each topping can only be chosen once

Answers

Answer:

24,024

Step-by-step explanation:

Calculation for How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings

The 4 pizza toppings from a menu of 14 toppings will be 14,13,12,11

Hence,

14*13*12*11=24,024

Therefore the numbers of way Rudy can choose 4 pizza toppings from a menu of 14 is 24,024

What is the Distance between 6+3i, 6-3i

Answers

2-8..........

ITS UR ANSWER!,

Evaluate x - 20 when x=3

Answers

Answer:

-17

Step-by-step explanation:

Plug in 3:

3 - 20 =

Solve:

3-20 = -17

Answer:

-17

Step-by-step explanation:

I replaced 3 for x, I solved the equation 3-20, which is equal to -17

jester has a piece of wood measuring 1 and 2/3 m.he needs to cut in pieces measuring 3/4 m. long.how many pieces of wood did jester cut.​

Answers

Answer:

2

Step-by-step explanation:

Given that,

Jester has a piece of wood measuring 1 and 2/3 m = 5/3 m

He needs to cut in pieces measuring 3/4 m

We need to find the number of pieces. Let there are x no. of pieces.

[tex]x=\dfrac{\dfrac{5}{3}}{\dfrac{3}{4}}\\\\=\dfrac{5}{3}\times \dfrac{4}{3}\\\\=2.23\[/tex]

or

x = 2

So, he will cut it into approx 2 pieces.

The ______ of a function consists of set of all output values

Answers

Domain and range :))))

Pleaseee help!!!!!!!!

Answers

Answer:

no

Step-by-step explanation:

no

The triangle is rotated 90 degrees clockwise around the pount (0,0)

Answers

Answer:

(2,6)

Step-by-step explanation:

Option:B

The triangle is rotated 90 degree clockwise around the point (0,0). The point is (-6,2) is made to rotate. The image so formed is at the point (2,6).

Can y’all help me solve this.
Please!!!!!!!

Answers

9514 1404 393

Answer:

  all statements are true

Step-by-step explanation:

The line 4y=-16 can be rewritten to standard form as ...

  y = -4 . . . . a horizontal line with all points having y-coordinate = -4

__

The line 3x = 27 can be rewritten to standard form as ...

  x = 9 . . . . a vertical line with all points having x-coordinate = 9.

__

All of the statements about these lines are true.

What is the image of (−8,−8) after a dilation by a scale factor of 1/2 centered at the origin?

Answers

Answer:

(-4,-4)

Step-by-step explanation:

Since this is centered at (0,0), we have to multiply the x and the y coordinates by the scale factor.

-8 × 1/2 = -4

joe boght 15 tolets. 1 was pure gold 2 were pure silver and the rest were wooden. how many wooden toilets were there?

Answers

12.
It is easy all you have to do is 15-3 because 1+2=3

Find the slope intercept equation of the line

PLEASE HELP ME!!!!!

Answers

Answer:

y = -x + 6

Step-by-step explanation:

Slope-intercept form:

y = mx + b, where m is slope and b is y-intercept

We see on the graph y-intercept is b = 6,  point (0.6)

To find the slope we need a second point, choosing point (5, 1)

Using slope formula:

m = (1- 6)/(5 - 0) = -5/5 = -1

So the line is:

y = -x + 6

Answer:

y = -4/5x + 5

Step-by-step explanation:

the formula for slope intercept is y=mx+b.

m represents the slope of the line and b is the y intercept. all you have to do is replace those variables.

the y intercept is the point where the line crosses the y-axis (the line going up and down on the graph). (0,5) is the y intercept and so 5 would replace b in y=mx+b

so far we have y=mx+5

The slope is the vertical change between two points is called the rise, and the horizontal change is called the run. Starting from a point on the line you would move vertically until you're in line with another point. In this case, let's just use (0,5) from before. You would go up four to line up with a point. Then, move horizontally to meet up with the point and count the units, which is five here. And so, the slope would be 4/5.

And then you get the equation:

y=4/5x+b

PRE CALC ON EDGE PLEASE HELP 100 PTS!!! IM TIMED

Answers

Answer:

The last option

Step-by-step explanation:

a is the hypotenuse, x is the adjacent, h is the opposite.

a^2 = h^2 + x^2

Subtract x^2 from both sides

h^2 = a^2 - x^2

Please gimme brainliest

I think it’s the last one

there are 36 playing tag at recess. this is 6 times as many playing hopscotch. which model shows this comparison?

i got the top one to the left (checking my answer)

Answers

Answer:

The top left one is correct.

Step-by-step explanation:

We can rewrite this as an algebraic expression simply so it's easier to read.

Let's say hopscotch is [tex]h[/tex]. Tag is 6 times [tex]h[/tex], or [tex]6h[/tex].

That means for every 1 unit of hopscotch, there are 6 units of tag.

The top left one is correct.

Multiply The polynomials. (3x^2+4x+4)(2x-4)

Answers

Answer:

6x^3 - 4x^2 - 8x - 16

Step-by-step explanation:

6x^3 + 8x^2 + 8x - 12x^2 - 16x - 16

combine

6x^3 - 4x^2 - 8x - 16

Name the factors in each of the following problems

Answers

Ok sure, lol.
Can’t see anything

Solve.
-|-10|+ (-3) + |5|=
A. -18
B-8
C. 8
D. 12
E18

Answers

Answer:

The answer is for-|-10|+(-3)+|5|=-8 which is B

SOMEONE PLEASE PLEASE HELP ME ON THIS!!

Answers

X=22

14 plus 8 gives you x

[tex]\frac{x}{20} =\frac{14}{8} \\x=\frac{14}{8} \times 20=35[/tex]Answer:

35

Step-by-step explanation:

The value of the square root of 14 is between which two integers?

Answers

3 and 4

3x3=9
4x4=16
14 is between 9 and 16.

please answer asap no trolls!

Answers

Answer:

Yes.

Step-by-step explanation:

3.5 + 5.5 > 7.8


Between what two multiples of ten is 328

Answers

Answer:

It's between 32 (which is 320) and 33 (which is 330).

Step-by-step explanation:

328 / 10 = 32.8

328 is between the multiple 320 and 330

I think this is right but want to check need help 25 points!!!

Answers

Answer:yes your Most definitely correct

Step-by-step explanation:

Consider a binomial experiment with n = 5 trials where the probability of success on a single trial is p = 0.30. (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.

Answers

Answer:

0.16807 ; 0.83193

Step-by-step explanation:

Given that:

Number of trials, n = 5

Probability of success, p = 0.30

P(r = 0)

Using the binomial probability relation :

P(x =r) = nCr * p^r * (1 - p)^(n - r)

(a) Find P(r = 0).

P(r = 0) = 5C0 * 0.3^0 * (0.7)^(5- 0)

= 1 * 1 * 0.16807

= 0.16807

(b) Find P(r ≥ 1) by using the complement rule

P(r ≥ 1) = 1 - P(r = 0)

P(r ≥ 1) = 1 - 0.16807

P(r ≥ 1) = 0.83193

A florist sells 3 roses for a total of $10. Each rose costs the same amount. What is the cost of 12 roses?

A. $9.60
В. $10.40
C. $14.00
D. $15.00​

Answers

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

if 3 roses   costs              10 dollars

3x4=12 roses.................10x4=40 dollars

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