W squared plus 7w plus 12 equals?

Answer 1

Written out

f(w) = w^2 + 7w + 12

there is no particular answer since it depends on what w is equal to.

normally this type of question is posited as "Solve for w with f(w) = 0?" or

to change its form to (ax + b)(cx + d)

if f(w) = w^2 + 7w + 12

and f(w) = 0

then

0 = w^2 + 7w + 12

simply look at the factors of 12

1 x 12

2 x 6

3 x 4

now consider

(w + a)(w + b) = w^2 + aw + bw + ab

= w^2 + (a+ b)w + ab

since you know

3 x 4 = 12 , and 3 + 4 = 7

this give you

0 = (w + 3) (w + 4) or f(w) = (w + 3)(w + 4)

solving for zero

w = either -3 or -4

as

(-3 + 3)(-3 + 4) = (0)(1) = 0

or

(-4 + 3)(-4 + 4) = (-1)(0) = 0

so depending on what you are actually looking for the answer is

w^2 + 7w +12 = (w + 3)(w + 4)

or

-3 and -4