Question

Factor 16x2 + 24x + 9.

Answer 1

1. Multiply first and third terms:
16*9=144

2. Factor 144 and find a pair of factors that adds up to the second term (24):
144=2*2*2*2*3*3
2*72, -2*-72
3*48, -3*-48
4*36, -4*-36
6*24, -6*-24
9*16, -9*-16
8*18, -8*-18
12*12, -12*-12

3. Rewrite polynomial:
16xx+24x+9
16xx+12x+12x+9

4. Factor pairs of terms (ie first and second, third and fourth):
4x(4x+3)+3(4x+3)

5. Combine common terms:
(4x+3)(4x+3) --> (4x+3)**2

Steps (short):
-since twice the product of the square roots of the first and third terms we can place it in the form (ax+c)**2 where a and c are the square roots of the first and third terms respectively

16xx+24x+9
(ax)**2+b+(c)**2
2*(sqrt(a**2)*sqrt(c**2))=b
2*(sqrt(16)*sqrt(9))=24

(sqrt(16)x+sqrt(9))**2
(4x+3)**2

Answer 2

it looks like a perfect square to me....or is that to big a hint