What is 16x2 plus 24x plus 9?

Answer 1

16xx+24x+9

Steps (long):

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