Free Printable 8.1-8.4 Review

1.

$15x^2-4x^3+9x$

What is the degree of the polynomial?

a)

6

b)

5

c)

3 (cubic)

d)

2 (quadratic)

2.

$7x^2+28x^4-12$

Name the polynomial by its degree and number of terms:

a)

quadratic trinomial

b)

quartic trinomial

c)

6th degree trinomial

d)

quadratic polynomial

3.

$144x^2y^3$

Write the name of the polynomial:

a)

cubic monomial

b)

quadratic monomial

c)

quartic monomial

d)

5th degree monomial

4.

$30x^2-24x\ +12$

What is the GCF of the the polynomial?

a)

$6x$

b)

$6$

c)

$12x$

d)

$6x^2$

5.

$2x^5+4x^4-10x^3+40x^2$

Rewrite the polynomial in factored form:

a)

$2x\left(x^4+2x^3-5x^2+20x\right)\$

b)

$2\left(x^5+2x^4-10x^3+20x^2\right)$

c)

$2x^2\left(x^3+2x^2-5x+20\right)$

d)

$2x^2\left(x^3+2x^2+5x+20\right)$

6.

$6x^3-2x^2+4-\left(2x^3+4x^2-5\right)$

Simplify the expression:

a)

$4x^3-2x^2-1$

b)

$8x^3+6x^2-1$

c)

$4x^3-2x^2+1$

d)

$4x^3-6x^2+9$

e)

$4x^3-2x^2+9$

7.

$6d^4+9d^3-12d^2$

Write this polynomial in factored form:

a)

$3d^2\left(2d^2+3d-4\right)$

b)

$3d\left(2d^3+3d^2-4d\right)$

c)

$3d^2\left(3d^2+6d-9\right)$

d)

$3\left(2d^4+3d^3-4d^2\right)$

8.

There is a circular garden in the middle of a square yard. The radius of the circle is 4x. The side length of the yard is 20x. What is the area of the part of the yard that is not covered by the circle (in factored form)?

a)

$4x\left(5\right)\ units^2$

b)

$8x^2\left(5-\pi\right)\ units^2$

c)

$16x\left(25+\pi\right)\ units^2$

d)

$16x^2\left(25-\pi\right)\ units^2$

9.

$-3z^2\left(z+2\right)-4\left(z^2-1\right)$

What is the simplified form of the expression:

a)

$-3z^3-4z^2-2$

b)

$-3z^3-10z^2-4$

c)

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

d)

$-13z^2+4$

10.

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

Simplify the expression completely. Use any of the four methods you learned.

a)

$2x^2-x-6$

b)

$2x^2\ -\ 6$

c)

$2x^2-7x-6$

d)

$2x^2+x-6$

11.

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

Use the box/table method to simplify the expression.

a)

$12x^2+x-6$

b)

$12x^2-6$

c)

$12x^2+18x+6$

d)

$12x^2-x-6$

e)

$12x^2+18x-6$

12.

$\left(4p-2\right)\left(p-4\right)$

Use the vertical method to simplify the expression:

a)

$4p^2+8$

b)

$4p^2+6p-16$

c)

$4p^2-18p+8$

d)

$4p^2-14p-6$

e)

$4p^2-6p+16$

13.

The radius of a cylinder is 3x-2 cm. The height of the cylinder is x+3 cm. What is the surface area of the cylinder in factored form?

a)

$2\pi\left(3x^2+10x-8\right)\ cm^2$

b)

$2\pi\left(12x^2+7x-2\right)\ cm^2$

c)

$2\pi\left(12x^2-2x+13\right)\ cm^2$

d)

$2\pi\left(12x^2-5x-2\right)\ cm^2$

14.

A soup can (shaped as a cylinder) has a radius of 2x-1 and a height of 3x. Planning the design and printing the labels takes time and money. Find the surface area of the soup can label in factored form.

a)

$6x^2\pi-3x\pi\ \ units^2$

b)

$12x^2\pi-6x\pi\ \ units^2$

c)

$\pi\left(16x^2-10x+1\right)\ units^2$

d)

$6x\pi\left(2x-1\right)\ \ units^2$

15.

What is the coefficient of the "x" term in the simplified form of (2x+4)² ?

(a)

16.

What is the constant in the simplified form of (x-6)² ?

(a)

17.

What is the constant in the simplified form of:

(2m-4) (2m+4) ?

(a)

18.

Which expression would you use to find the product of 38 and 42 using mental math?

a)

$\left(30+8\right)\left(40+2\right)$

b)

$\left(30+8\right)\ \left(50-8\right)$

c)

$\left(40-2\right)\left(40+2\right)$

d)

$\left(40-2\right)\left(50-8\right)$

19.

Which of the following results in a binomial when simplified? Check all that apply.

a)

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

b)

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

c)

$\left(s-13\right)\left(s+13\right)$

d)

$\left(m-7\right)\left(7-m\right)$

20.

What is the volume of a cube with a side length of $x^2-3$ inches?

a)

$x^6-27\ in^3$

b)

$x^6-9x^4+27x^2-27\ in^3$

c)

$x^4+6x^2-27\ in^3$

d)

$x^6+9x^4-27x^2-27\ in^3$

8.1-8.4 Review

Total questions: 20

Worksheet time: 5hrs 0mins

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