Question

What is the factored form of the expression 9x2 + 6x + 1?

O (3x - 1)2
O (3x + 1)2
O (9x + 1)2
O (9x - 1)

Answer 1

(3x + 1)^2

Explanation:

The first and last terms are perfect squares. From its structure, this is a perfect square trinomial.

All of the symbols in the expression 9x2 + 6x + 1 are positive, so use the rule for the square of the sum of two terms.

In the given expression, a2 = 9x2 and b2 = 1, so a = 3x and b = 1.

2ab = 2(3x)

= 6x

This result matches the middle term in the polynomial expression, 6x, so apply the rule for the square of the sum of two terms.

The expression 9x2 + 6x + 1 is equal to (3x + 1)2.

Answer 2

(3x + 1)²

Explanation:

Given

9x² + 6x + 1 ← is a perfect square of the form

(ax + b)² = a²x² + 2abx + b²

Compare like terms to find a and b

a²x² = 9x² ⇒ a² = 9 ⇒ a =
`√(9)` = 3

b² = 1 ⇒ b =
`√(1)` = 1

and 2ab = 2 × 3 × 1 = 6

Thus

9x² + 6x + 1 = (3x + 1)²