BECE Algebraic Expressions and Equations 3

Question 1

Factorise completely: 6x² + 9x.

Accepted Answer

3x(2x + 3)

Answer

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?

Accepted Answer

5

Answer

m + 2 = 7, so m = 5.

Question 3

Which expression is equivalent to (x + 3)(x − 3)?

Accepted Answer

x² − 9

Answer

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?

Accepted Answer

5

Answer

3n − 2 = 13, so 3n = 15 and n = 5.

Question 5

Simplify: (5x³y²) ÷ (x²y).

Accepted Answer

5xy

Answer

Subtract exponents: x³÷x² = x and y²÷y = y, giving 5xy.

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