Question

Determine which polynomial is a perfect square trinomial. 4x2 − 12x 9 16x2 24x − 9 4a2 − 10a 25 36b2 − 24b − 16.

Answer 1

This $4x^2 - 12x + 9$ factors into $(2x - 3)^2$, and is thus a perfect square trinomial.

What is a perfect square?

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

Trinomial $Ax^2 + Bx + C$ is a perfect square if

A > 0

C > 0

B = ±2√A√C

1. $36b^2 - 24b - 16$

C < 0

2. $4a^2 - 10a + 25$

2√A√C = 2×2×5

              = 20,

B = −10

3. $16x^2 + 24x - 9$

not a perfect square,

C < 0

4. $4x^2- 12x + 9$

perfect square

A>0,

C>0,

2√A√C = 2×2×3

-B = 12

= $(2x - 3)^2$

Thus,  $4x^2- 12x + 9$ the polynomial is a perfect square trinomial.

Learn more about perfect square;

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