Question

find the value for b that will make the trinomial 4x^2+bx+81 a perfect square trinomial. FACTOR the resulting:

Answer 1

Step-by-step explanation:

Given the below trinomial;

`4x^2+bx+81`

We're asked to determine the value of b to make the above trinomial a perfect square.

To solve the above, note that perfect square trinomials are generally written in the below form;

`(ax\pm b)^2=(ax)^2\pm2axb+b^2`

Let's rewrite the given trinomial in the above form, we'll have;

`4x^2+bx+81=(2x)^2+2bx+9^2`

If we compare both expressions, we can observe the below;