Question

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

Answer 1

Answer:

($2x + 3)^{2}$

Step-by-step 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~