Answer:
([tex]2x + 3)^{2}[/tex]
Step-by-step explanation:
[tex]f(x) = 4x^{2} + 12x + 9[/tex]
Factor the expression by grouping. First, the expression needs to be rewritten [tex]4x^{2} + ax + bx + 9[/tex]. To find a and b, set up a system to be solved.
[tex]a + b = 12\\ab = 4 x 9 = 36[/tex]
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 [tex]4x^{2} + 12x + 9[/tex] as [tex](4x^{2} + 6x) + (6x + 9)[/tex]
[tex](4x^{2} + 6x) + (6x + 9)[/tex]
Factor out 2x in the first and 3 in the second group.
[tex]2x (2x + 3) + 3 (2x + 3)[/tex]
Factor out the common term 2x + 3 by using the distributive property.
[tex](2x + 3) (2x + 3)[/tex]
Rewrite as a binomial square.
[tex](2x + 3)^{2}[/tex]
Hope it helps and have a great day! =D
~sunshine~
