Algebra Test Polynomials and Factoring 2

Question 1

Multiply: (x - 4)(x + 4).

Accepted Answer

x² - 16

Answer

This is a difference of squares: (a - b)(a + b) = a² - b² = x² - 16.

Question 2

Factor: x² - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

x² - 9 = x² - 3² is a difference of squares, factoring as (x + 3)(x - 3).

Question 3

Subtract: (4x² - 3x + 2) - (x² + 2x - 5).

Accepted Answer

3x² - 5x + 7

Answer

Distribute the negative: 4x² - 3x + 2 - x² - 2x + 5 = 3x² - 5x + 7.

Question 4

What is the leading coefficient of -3x⁴ + 2x² - x?

Accepted Answer

-3

Answer

The leading coefficient is the coefficient of the highest-degree term, which is -3.

Question 5

Factor: 2x² - 8x.

Accepted Answer

2x(x - 4)

Answer

Factor out 2x: 2x(x - 4).

Algebra Test Practice Test