Free Printable Unit 4 TEST

1.

See picture

a)

81y^{4\ }+\ 216y^3\ +\ 216y^2\ +\ 96y\ +\ 16

b)

$81y^{3\ }+\ 216y^2\ +\ 216y^1\ +\ 96y\ +\ 16$

c)

$64y^{4\ }+\ 81y^3\ +\ 81y^2\ +\ 48y\ +\ 9$

d)

$81y^{4\ }+\ 96y^3\ +\ 216y^2\ +\ 64y\ +\ 25$

2.

Select the next two steps to prove the special product pattern for the square of a binomial. Note: the answer choices below may not be in order.
$(x+y)^2=(x+y)(x+y)$

a)

$x^2+2xy^1+y$

b)

$x^2+xy+xy+y^2$

c)

$x^2+2xy+y^2$

d)

$x^4+xy^3+xy^2+y^1$

3.

Divide $2x^4+3x^3−5x+6\ \ \ \div\ \ \ x^2+3x−2.$

a)

$2x^2−3x+13+\frac{-50x+\ 32}{x^2\ +3x\ -2}$

b)

$x^2−6x+12+\frac{-25x+\ 16}{2x^2\ +4x\ -8}$

c)

$4x^2+6x+26+\frac{-16x+\ 7}{x^2\ +5x\ +11}$

d)

$2x^2+3x-13+\frac{-30x+\ 48}{x^2\ -3x\ +4}$

4.

Use synthetic division to evaluate the function $f\left(x\right)=-2x^3\ +\ 3x\ -6\ when\ x=-5$

a)

334

b)

187

c)

216

d)

229

e)

292

5.

Factor the function completely:
$x^{3\ }+3x^2-x-3$

a)

$(x+1)(x+1)(x-3)$

b)

$(x+1)(x+−1)(x+3)$

c)

$(x-1)(x+−1)(x+3)$

d)

$(x^2+1)(x-1)(x+3)$

6.

Factor
$f\left(x\right)=4x^3-24x^2+36x$

a)

$4x\left(x-3\right)^2$

b)

$4x\left(x+3\right)^{ }\left(x-3\right)$

c)

$9x\left(x-18\right)^2$

d)

$9x\left(x+_{ }3\right)^{ }\left(x-3\right)$

7.

Use your factorization to find the zeros of the function.
$f\left(x\right)\ =\ 4x^3-24x^2+36x$

a)

0

b)

2

c)

3

d)

6

e)

9

8.

Find all zeros of $f\left(x\right)=4x^3+64x$ by completely factoring the polynomial.

a)

2

b)

0

c)

$\pm4i$

d)

$\pm2i$

e)

$\pm8i$

9.

Write a polynomial function $f$ of least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and $3-i$ .

a)

$x^3-10x^2+34x-40$

b)

$2x^3-35x^2+36x-20$

c)

$x^3+10x^2+34x-30$

d)

$x^3+20x^2+28x+40$

e)

$x^3+10x^2-34x+40$

10.

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. $4,\ -\sqrt{5},\ -5$

a)

$x^4+x^{3\ }-25x^2-5x+100$

b)

$x^4+30x^{3\ }-5x^2-5x+10$

c)

$x^4+30x^{3\ }+5x^2+5x+10$

d)

$x^4+2x^{3\ }+25x^2-10x+75$

11.

Find the product of $\left(c^8-6\right)\left(c^2-4c-2\right)$

a)

$c^{10}-4c^9-2c^8-6c^2+24c+12$

b)

$c^{10}-2c^8-6c^4+24c^2+12$

c)

$c^{10}-4c^8-2c^6+6c^4+24c+12$

d)

$c^{10}+4c^8-2c^7-6c^2+24c+12$

12.

The graphs of $f\left(x\right)=x^{4\ }and\ g\left(x\right)=\left(x+4\right)^4$ are shown in the picture. Select the zeros that each function has.

a)

f(x) has a zero at 0

b)

g(x) has a zero at -4

c)

f(x) has a zero at 4

d)

g(x) has a zero at 4

e)

g(x) has a zero at 8

13.

(part 1) The volume V (in cubic feet) of a hot tub is modeled by the polynomial function $v\left(x\right)=x^3-10x^2+11x+70$ where x is the length of the hot tub.

Explain how you know x = −5 is NOT a possible rational zero.

4 lines

14.

(part 2) The volume V (in cubic feet) of a hot tub is modeled by the polynomial function $V\left(x\right)=x^3-10x^2+11x+70$ where x is the length of the hot tub.

Factor V(x) completely.

a)

$V\left(x\right)=\left(x-7\right)\left(x-5\right)\left(x+2\right)$

b)

$V\left(x\right)=\left(x+7\right)\left(x+5\right)\left(x-2\right)$

c)

$V\left(x\right)=\left(x-5\right)\left(x+\ 7\right)\left(x+10\right)$

d)

$V\left(x\right)=\left(x-14\right)\left(x+10\right)\left(x+2\right)$

15.

Divide $\left(4x^3+20x^2+12x-16\right)\ \ \div\ \ \left(x-4\right)$

a)

$4x^2+36x\ +156+\frac{608}{x-4}$

b)

$2x^2+36x\ +232+\frac{448}{x-2}$

c)

$4x^2+18x\ +64+\frac{608}{x-8}$

d)

$2x^2+24x\ +32+\frac{636}{x-6}$

16.

Find the product of $\left(3x+1\right)^3$

a)

$27x^3+27x^2+9x+1$

b)

$9x^3+27x^2-9x+3$

c)

$27x^3-18x^2+9x-1$

d)

$18x^3-36x^2+27x-1$

Unit 4 TEST

Total questions: 16

Worksheet time: 4hrs 0mins

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