Question

9x² + 6x + 1 is equal to ______.

Options

• (3x + 1) (3x – 1)

• (x + 3) (9x + 1)

• (9x + 3) (x + 1)

• (3x + 1) (3x + 1)

Answer 1

9x² + 6x + 1 is equal to (3x + 1) (3x + 1).

Explanation:

To factorise 9x² + 6x + 1, notice that the expression is a perfect square trinomial.

Step 1: Recognise the pattern.

We observe that:

(3x)² = 9x²,

2 · 3x · 1 = 6x,

1² = 1

This is a perfect square trinomial, which can be factored as (3x + 1)²

Step 2: Final factorisation.

Thus, the factorization is (3x + 1) (3x + 1) = (3x + 1)²