When we divide polynomials, there are two different scenarios. The first and easier of the two involves dividing a polynomial by a monomial. For this type of problem, we setup a fraction and divide each term of the polynomial by the monomial. The second and harder scenario involves dividing polynomials when neither is a monomial. For this type of problem, we generally use polynomial long division.

Test Objectives
• Demonstrate the ability to divide a polynomial by a monomial
• Demonstrate the ability to setup a polynomial long division
• Demonstrate the ability to divide polynomials when remainders are involved
Polynomial Long Division Practice Test:

#1:

Instructions: Find each quotient.

a) (7n4 - 43n3 - 2n2 + 13n + 36) ÷ (7n - 8)

#2:

Instructions: Find each quotient.

a) (58r - 24r2 + 40 + 2r3) ÷ (r - 8)

#3:

Instructions: Find each quotient.

a) (42x4 - 63x3 + 3x2 + 39x - 14) ÷ (6x - 3)

#4:

Instructions: Find each quotient.

a) (-32x5 - 8x4 - 28x2 + 72x + 60) ÷ (-8x2 + 12)

#5:

Instructions: Find each quotient.

a) (-36x4 - 24x3 - 40x + 100) ÷ (12x2 + 20)

Written Solutions:

#1:

Solutions:

a) $$n^3 - 5n^2 - 6n - 5 + \frac{-4}{7n - 8}$$

#2:

Solutions:

a) $$2r^2 - 8r - 6 + \frac{-8}{r - 8}$$

#3:

Solutions:

a) $$7x^3-7x^2-3x+5+\frac{1}{6x-3}$$

#4:

Solutions:

a) $$4x^3+x^2+6x+5$$

#5:

Solutions:

a) $$-3x^2-2x+5$$