Algebra Test Polynomials 1 — Questions and Answers
Question 1: What is the degree of 4x³ - 2x² + 7x - 1?
- 1
- 2
- 3 (Correct answer)
- 4
Correct answer: 3
The degree is the highest exponent, which is 3.
Question 2: Simplify: (3x² + 2x - 1) + (x² - 4x + 5)
- 4x² - 2x + 4 (Correct answer)
- 4x² + 6x - 6
- 2x² - 2x + 4
- 4x² - 2x - 4
Correct answer: 4x² - 2x + 4
Combine like terms: (3+1)x² = 4x², (2-4)x = -2x, (-1+5) = 4, giving 4x² - 2x + 4.
Question 3: What is the leading coefficient of -5x⁴ + 3x² - x + 8?
- 8
- 3
- -1
- -5 (Correct answer)
Correct answer: -5
The leading coefficient is the coefficient of the highest-degree term, which is -5.
Question 4: Multiply: (x + 3)(x - 2)
- x² - 6
- x² + x - 6 (Correct answer)
- x² - x - 6
- x² + x + 6
Correct answer: x² + x - 6
Using FOIL: x² - 2x + 3x - 6 = x² + x - 6.
Question 5: What is (2x²)(3x³)?
- 5x⁵
- 6x⁵ (Correct answer)
- 5x⁶
- 6x⁶
Correct answer: 6x⁵
Multiply coefficients 2 × 3 = 6 and add exponents 2 + 3 = 5, giving 6x⁵.
Question 6: Factor completely: x² - 16
- (x - 4)²
- (x + 4)²
- (x - 4)(x + 4) (Correct answer)
- (x - 2)(x + 8)
Correct answer: (x - 4)(x + 4)
This is a difference of squares: x² - 16 = (x - 4)(x + 4).
Algebra Test Polynomials 1
What is the degree of 4x³ - 2x² + 7x - 1?