Question

Please help me I’ve got to get this done!

Answer 1

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`2x + 3)^(2)`

Explanation:

`f(x) = 4x^(2) + 12x + 9`

Factor the expression by grouping. First, the expression needs to be rewritten
`4x^(2) + ax + bx + 9`. To find a and b, set up a system to be solved.

`a + b = 12\\ab = 4 x 9 = 36`

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 36.

1,36

2,18

3,12

4,9

6,6

Calculate the sum for each pair.

1 + 36 = 37

2 + 18 = 20

3 + 12 = 15

4 + 9 = 13

6 + 6 = 12

The solution is the pair that gives sum 12.

a=6

b=6

Rewrite
`4x^(2) + 12x + 9` as
`(4x^(2) + 6x) + (6x + 9)`

`(4x^(2) + 6x) + (6x + 9)`

Factor out 2x in the first and 3 in the second group.

`2x (2x + 3) + 3 (2x + 3)`

Factor out the common term 2x + 3 by using the distributive property.

`(2x + 3) (2x + 3)`

Rewrite as a binomial square.

`(2x + 3)^(2)`

Hope it helps and have a great day! =D

~sunshine~