Algebra Test Polynomials and Factoring 1 — Questions and Answers
Question 1: Simplify: (3x² + 2x - 1) + (x² - 4x + 5).
- 4x² - 2x + 4 (Correct answer)
- 4x² + 2x + 4
- 2x² - 2x + 4
- 4x² - 2x - 4
Correct answer: 4x² - 2x + 4
Combine like terms: (3+1)x² + (2-4)x + (-1+5) = 4x² - 2x + 4.
Question 2: What is the degree of the polynomial 5x⁴ - 3x² + 7x - 2?
- 2
- 3
- 4 (Correct answer)
- 5
Correct answer: 4
The degree is the highest power of the variable, which is 4.
Question 3: Multiply: (x + 3)(x - 2).
- x² + 5x - 6
- x² - x - 6
- x² + x - 6 (Correct answer)
- x² - 5x + 6
Correct answer: x² + x - 6
Use FOIL: x² - 2x + 3x - 6 = x² + x - 6.
Question 4: Factor out the GCF: 6x³ + 9x².
- 3x(2x² + 3x)
- 3x²(2x + 3) (Correct answer)
- 6x²(x + 9)
- 9x²(x + 1)
Correct answer: 3x²(2x + 3)
The GCF of 6x³ and 9x² is 3x², giving 3x²(2x + 3).
Question 5: Expand: (2x + 1)².
- 4x² + 1
- 4x² + 2x + 1
- 4x² + 4x + 1 (Correct answer)
- 2x² + 4x + 1
Correct answer: 4x² + 4x + 1
Using (a + b)² = a² + 2ab + b²: (2x)² + 2(2x)(1) + 1² = 4x² + 4x + 1.
Question 6: A polynomial with exactly 3 terms is called a:
- Monomial
- Binomial
- Trinomial (Correct answer)
- Quadrinomial
Correct answer: Trinomial
A trinomial is a polynomial with exactly three terms.
Algebra Test Polynomials and Factoring 1
Simplify: (3x² + 2x - 1) + (x² - 4x + 5).