To divide the function f(x) by (x2-4x-12), we find that the quotient is Q(x) and the remainder is (x+6). If f(-2)=a and f(6)=b, what is the value of b/a?
2 answers
help plz
I recall oobleck answering this yesterday, but with the "search" feature of this webpage being useless I can't find it, I will do it
f(x) / (x^2 - 4x - 12) = Q(x) + (x+6)/(x^2 - 4x - 12)
did you notice x^2 - 4x - 12 = (x-6)(x+2) ??
multiply each term by that denominator
f(x) = Q(x) * ((x-6)(x+2)) + x+6
f(-2) = 0 + -2+6 = a,
so a = 4
f(6) - 0 + 6+6 = b,
so b = 12
then b/a = 12/4 = 3
f(x) / (x^2 - 4x - 12) = Q(x) + (x+6)/(x^2 - 4x - 12)
did you notice x^2 - 4x - 12 = (x-6)(x+2) ??
multiply each term by that denominator
f(x) = Q(x) * ((x-6)(x+2)) + x+6
f(-2) = 0 + -2+6 = a,
so a = 4
f(6) - 0 + 6+6 = b,
so b = 12
then b/a = 12/4 = 3