BECE Algebraic Expressions and Equations 3 — Questions and Answers
Question 1: Factorise completely: 6x² + 9x.
- 3x(2x + 3) (Correct answer)
- 3(2x² + 3x)
- 6x(x + 3)
- x(6x + 9)
Correct answer: 3x(2x + 3)
The HCF of 6x² and 9x is 3x, giving 3x(2x + 3).
Question 2: If 3(m + 2) = 21, what is the value of m?
Correct answer: 5
m + 2 = 7, so m = 5.
Question 3: Which expression is equivalent to (x + 3)(x − 3)?
- x² − 9 (Correct answer)
- x² + 9
- x² − 6x + 9
- x² + 6x − 9
Correct answer: x² − 9
Using difference of two squares: (x + 3)(x − 3) = x² − 9.
Question 4: Two less than three times a number equals 13. What is the number?
Correct answer: 5
3n − 2 = 13, so 3n = 15 and n = 5.
Question 5: Simplify: (5x³y²) ÷ (x²y).
- 5xy (Correct answer)
- 5x²y
- 5xy²
- 5x³y
Correct answer: 5xy
Subtract exponents: x³÷x² = x and y²÷y = y, giving 5xy.
Question 6: What value of x satisfies 2x + 7 = 15?
Correct answer: 4
2x = 15 − 7 = 8, so x = 4.
Question 7: Expand and simplify: (2x + 1)².
- 4x² + 4x + 1 (Correct answer)
- 4x² + 1
- 2x² + 4x + 1
- 4x² + 2x + 1
Correct answer: 4x² + 4x + 1
(2x + 1)² = 4x² + 2(2x)(1) + 1 = 4x² + 4x + 1.
