Question

Given the following perfect square trinomial, fill in the missing term. (Do not type the variable in the blank.)

4x2 + ___x + 49

Answer 1

The perfect square trinomial is given by:

`4x^2+28x+49`

Explanation:

We are given a expression as follows:

`4x^2+-----x+49`

we know that a perfect square trinomial is of the form:

`(ax)^2+2abx+b^2`

Here we could represent our given expression as:

`4x^2+-----x+49=(2x)^2+-----x+7^2`

i.e.

a=2 , b=7

Hence, we have:

`2ab=2* 2* 7\\\\2ab=28`

Hence, the perfect square trinomial is:

`4x^2+28x+49`

Answer 2

a perfect square trinomial has a factor that is identical to the other factor. In this case, from the first term, the factor is composed of 2x while from the third term, there is a term 7 involved. In this case, the factor is 2x + 7. so the second term has to be 2*(2*7) equal to 28