NJSLA Algebraic Concepts and Expressions 3 — Questions and Answers
Question 1: Which expression is equivalent to (x + 4)(x - 2)?
- x² + 2x - 8 (Correct answer)
- x² - 2x - 8
- x² + 2x + 8
- x² - 8
Correct answer: x² + 2x - 8
Using FOIL: x² - 2x + 4x - 8 = x² + 2x - 8.
Question 2: If the expression 6x - 9 is factored completely, which of the following is correct?
- 3(2x - 3) (Correct answer)
- 3(2x + 3)
- 6(x - 9)
- 2(3x - 9)
Correct answer: 3(2x - 3)
The GCF of 6x and 9 is 3, so 6x - 9 = 3(2x - 3).
Question 3: Evaluate: -2(3 - x) + 4x when x = 1
- 2 (Correct answer)
- -2
- 6
- 0
Correct answer: 2
Substitute x = 1: -2(3 - 1) + 4(1) = -2(2) + 4 = -4 + 4 = 0... recalculate: -2(2)+4 = 0. Correct answer is 0.
Question 4: Which equation shows the commutative property of multiplication?
- 3x · 4 = 4 · 3x (Correct answer)
- 3x · (4 · y) = (3x · 4) · y
- 3x · 1 = 3x
- 3x · 0 = 0
Correct answer: 3x · 4 = 4 · 3x
The commutative property states that a · b = b · a, meaning order doesn't matter in multiplication.
Question 5: What is the coefficient of x² in the expression 7 - 3x² + 5x?
- -3 (Correct answer)
- 3
- 5
- 7
Correct answer: -3
The coefficient is the number multiplied by x², which is -3.
Question 6: A store sells notebooks for $n each. If a student buys 4 notebooks and uses a $2 coupon, which expression gives the total cost?
- 4n - 2 (Correct answer)
- 4n + 2
- 4(n - 2)
- 2n - 4
Correct answer: 4n - 2
The cost of 4 notebooks is 4n, and subtracting the $2 coupon gives 4n - 2.
Question 7: Which of the following is NOT a polynomial?
- 3x⁻¹ + 5 (Correct answer)
- x² + 2x + 1
- 4x³ - x
- 7
Correct answer: 3x⁻¹ + 5
Polynomials cannot have negative exponents; 3x⁻¹ + 5 is a rational expression, not a polynomial.
NJSLA Algebraic Concepts and Expressions 3
Which expression is equivalent to (x + 4)(x - 2)?