Algebra Test Polynomials and Factoring 2 — Questions and Answers
Question 1: Multiply: (x - 4)(x + 4).
- x² - 16 (Correct answer)
- x² + 16
- x² - 8x + 16
- x² + 8x - 16
Correct answer: x² - 16
This is a difference of squares: (a - b)(a + b) = a² - b² = x² - 16.
Question 2: Factor: x² - 9.
- (x - 3)(x - 3)
- (x + 9)(x - 1)
- (x + 3)(x - 3) (Correct answer)
- (x - 9)(x + 1)
Correct answer: (x + 3)(x - 3)
x² - 9 = x² - 3² is a difference of squares, factoring as (x + 3)(x - 3).
Question 3: Subtract: (4x² - 3x + 2) - (x² + 2x - 5).
- 3x² - 5x + 7 (Correct answer)
- 3x² + 5x - 7
- 5x² - 5x + 7
- 3x² - x + 7
Correct answer: 3x² - 5x + 7
Distribute the negative: 4x² - 3x + 2 - x² - 2x + 5 = 3x² - 5x + 7.
Question 4: What is the leading coefficient of -3x⁴ + 2x² - x?
- 4
- -3 (Correct answer)
- 3
- 1
Correct answer: -3
The leading coefficient is the coefficient of the highest-degree term, which is -3.
Question 5: Factor: 2x² - 8x.
- 2x(x - 4) (Correct answer)
- 2x(x + 4)
- x(2x - 8)
- 2(x² - 4x)
Correct answer: 2x(x - 4)
Factor out 2x: 2x(x - 4).
Question 6: Which is the correct expansion of (x + 5)(x - 3)?
- x² - 2x - 15
- x² + 2x - 15 (Correct answer)
- x² + 2x + 15
- x² - 2x + 15
Correct answer: x² + 2x - 15
FOIL: x² - 3x + 5x - 15 = x² + 2x - 15.
Algebra Test Polynomials and Factoring 2
Multiply: (x - 4)(x + 4).