Free Printable Unit 8 Review #3 Final

1.

Subtract
$(4x^3-2x^2+8)-(-8x^2+x-5)$

a)

$-4x^3-2x^2+x-3$

b)

$4x^3-10x^2-x+3$

c)

$4x^3+6x^2-x+13$

d)

$4x^3+6x^2+x+13$

2.

Factor $8x^3-125$

a)

$(2x-5)(4x^2+10x+25)$

b)

$(2x+5)(4x^2-10x+25)$

c)

$(x-5)(x^2+5x+25)$

d)

$(4x-5)(16x^2+20x+25)$

3.

Factor $x^3-3x^2-25x+75$

a)

$\left(x+3\right)\left(x-5\right)\left(x+5\right)$

b)

$\left(x-3\right)\left(x^2+25\right)$

c)

$\left(x+3\right)\left(x^2+25\right)$

d)

$\left(x-3\right)\left(x-5\right)\left(x+5\right)$

4.

What is the leading coefficient? $P\left(x\right)=-12x^4+9x^2-10+8x^5$

a)

9

b)

8

c)

-12

d)

-10

5.

Classify the polynomial by degree: $P (x) = 8 x^{5} - 12 x^{4} + 9 x^{3} - 10$

a)

cubic

b)

quadratic

c)

quartic

d)

quintic

6.

Classify the polynomial by the number of terms:
$P(x)=8x^5-12x^4+9x^3-10$

a)

binomial

b)

trinomial

c)

polynomial of 4 terms

d)

polynomial of 5 terms

7.

What are the end behaviors of the polynomial
$P(x)=8x^5-12x^4+9x^3-10$

a)

rises left, rises right

b)

rises left, falls right

c)

falls left, falls right

d)

falls left, rises right

8.

Solve by factoring. Be sure to identify any multiplicities

$x^4-7x^3-60x^2=0$

a)

$\left\{-12,\ 0\ m2,\ 5\right\}$

b)

$\left\{-5,\ 0\ m2,\ 12\right\}$

c)

$\left\{-10,\ 0\ m4,\ 6\right\}$

d)

$\left\{-6,\ 0\ m2,\ 10\right\}$

9.

Solve by factoring.

$x^4-36=0$

a)

$\left\{\pm3,\ \pm\sqrt{3}\right\}$

b)

$\left\{\pm\sqrt{6},\ \pm i\sqrt{6}\right\}$

c)

$\left\{\pm\sqrt{6},\ 6i\right\}$

d)

$\left\{\pm6i,\ \pm6\right\}$

10.

Given $P\left(x\right)=4x^4-8x^2-25x+50$

find $P\left(1\right)$ using synthetic substitution.

a)

50

b)

29

c)

31

d)

21

11.

Given $P(x)=4x^4-8x^2-25x+50$

Find $P\left(-2\right)$ using synthetic substitution

a)

132

b)

36

c)

4

d)

142

12.

Select all roots including the real, multiplicities, and complex roots. (You may have more than 1 answer.)

$x^4+6x^3+4x^2-30x-45=0$

a)

$-3\ m2$

b)

$3\ m2$

c)

$\pm5i$

d)

$\pm5$

e)

$\pm\sqrt{5}$

13.

Select all roots including the real, multiplicities, and complex roots. (You may have more than 1 answer.)
$x^4-2x^3+13x^2-32x-48=0$

a)

3

b)

1

c)

-1

d)

$\pm4$

e)

$\pm4i$

14.

Select all roots including the real, multiplicities, and complex roots. (You may have more than 1 answer.)
One root is given to you.
$f(x)=x^3+5x^2+2x-8\ \ \ ;\ \ \ \ (x+4)$

a)

-2

b)

2

c)

1

d)

-1

e)

-4

Unit 8 Review #3 Final

Total questions: 14

Worksheet time: 4hrs 30mins

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