Algebra Test Polynomials and Factoring 3

Question 1

Factor completely: 3x³ - 12x.

Accepted Answer

3x(x + 2)(x - 2)

Answer

Factor out 3x to get 3x(x² - 4), then factor the difference of squares to get 3x(x + 2)(x - 2).

Question 2

What is the result of (2x + 3)(3x - 1)?

Accepted Answer

6x² + 7x - 3

Answer

FOIL: 6x² - 2x + 9x - 3 = 6x² + 7x - 3.

Question 3

Factor: x² - 2x - 8.

Accepted Answer

(x - 4)(x + 2)

Answer

Find two numbers that multiply to -8 and add to -2: -4 and 2, giving (x - 4)(x + 2).

Question 4

Factor 4x² + 12x + 9.

Accepted Answer

(2x + 3)²

Answer

This is a perfect square trinomial: (2x)² + 2(2x)(3) + 3² = (2x + 3)².

Question 5

Divide: (6x³ - 3x) ÷ 3x.

Accepted Answer

2x² - 1

Answer

Divide each term: 6x³/3x - 3x/3x = 2x² - 1.

Algebra Test Practice Test