NJSLA Algebraic Concepts and Expressions 4 — Questions and Answers
Question 1: What is the degree of the polynomial 5x³ - 2x⁴ + x - 7?
- 4 (Correct answer)
- 3
- 1
- 7
Correct answer: 4
The degree is the highest exponent, which is 4 (from the -2x⁴ term).
Question 2: Simplify: (5x² - 3x + 2) - (2x² + x - 4)
- 3x² - 4x + 6 (Correct answer)
- 3x² - 2x - 2
- 7x² - 4x + 6
- 3x² - 4x - 2
Correct answer: 3x² - 4x + 6
Distribute the negative sign and combine like terms: 5x²-2x²=3x², -3x-x=-4x, 2+4=6.
Question 3: For what value of x does the expression 3x + 7 equal 22?
- 5 (Correct answer)
- 7
- 3
- 9
Correct answer: 5
Solve 3x + 7 = 22: subtract 7 to get 3x = 15, then divide by 3 to get x = 5.
Question 4: Which expression is equivalent to x² - 9?
- (x + 3)(x - 3) (Correct answer)
- (x - 3)²
- (x + 9)(x - 1)
- (x - 3)(x - 3)
Correct answer: (x + 3)(x - 3)
x² - 9 is a difference of squares: a² - b² = (a + b)(a - b), so x² - 9 = (x + 3)(x - 3).
Question 5: If 2(x + 3) = 14, what is the value of x + 3?
- 7 (Correct answer)
- 4
- 11
- 5
Correct answer: 7
Dividing both sides by 2 gives x + 3 = 7, without needing to solve for x alone.
Question 6: A formula for simple interest is I = prt. Which expression gives p in terms of I, r, and t?
- I/(rt) (Correct answer)
- Irt
- I - rt
- rt/I
Correct answer: I/(rt)
To isolate p, divide both sides of I = prt by rt, giving p = I/(rt).
Question 7: Which term is a 'like term' with 4x²y?
- -7x²y (Correct answer)
- 4xy²
- 4x²
- 7xy
Correct answer: -7x²y
Like terms must have the same variables raised to the same powers; -7x²y matches x²y.
NJSLA Algebraic Concepts and Expressions 4
What is the degree of the polynomial 5x³ - 2x⁴ + x - 7?