Question

I am so confused Please Help it is DUE NOW!!

Select the polynomial that is a perfect square trinomial.
9x^2 + 9x + 1
36b^2 − 24b + 8
16x^2 + 24x + 9
4a^2 − 10a + 25

Answer 1

The third answer listed:

`16x^2+24x+9`

Explanation:

The trinomial:

`16x^2+24x+9`

can be factored out as follows:

`16x^2+24x+9\\(4x)^2+24x+3^2\\(4x)^2+12x+12x+3^2\\4x(4x+3)+3(4x+3)\\(4x+3)\,(4x+3)\\(4x+3)^2`

which as can be seen,is the perfect square of a binomial, so this trinomial is what is called a perfect square trinomial.

Answer 2

16x^2 + 24x + 9

Explanation:

perfect square trinomial is of the form

a^2 + 2 * a * b + b^2

9x^2 + 9x + 1 = (3x)^2 + 3*3x*1 + 1^2 not a perfect square trinomial

36b^2 − 24b + 8 = ( 6b)^2 -2 * 6b *2 + ( 2 sqrt(2)) ^2 not a perfect square trinomial

16x^2 + 24x + 9 = ( 4x) ^2 + 2 * ( 4x) * 3 + 3^2 = perfect square trinomial

4a^2 − 10a + 25 = ( 2a) ^2 - 1 * 2a *5 + 5^2 not a perfect square trinomial