Question

The function f(x) = x² +16x - 36 can be factored into the form

ƒ(x) = (x + B) (x − C).
-
What are the values for B and C?
NOTE: Enter your answers as positive integer values.
B =
C=

Answer 1

B=18 and C=2

Explanation:

To find the possible factors of the function, recall that a*c must equal u*v and b must equal u+v:

So,

`a=1\\b=16\\c=-36\\u=-2\\v=18`

`(1)(-36)=-36=(-2)(18)`

and

`16=(-2)+(18)`

f(x) can then be rewritten as:

`f(x)=x^2-2x+18x-36\\f(x)=(x^2-2x)+(18x-36)\\f(x)=x(x-2)+18(x-2)\\f(x)=(x+18)(x-2)`

So,

B=18 and C=2