SOLUTION: If x+p is a factor of ax*+bx+3, show that p(b-ap)=3.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If x+p is a factor of ax*+bx+3, show that p(b-ap)=3.      Log On


   

Question 100274: If x+p is a factor of ax*+bx+3, show that p(b-ap)=3.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Before I start, if ax%5E2%2Bbx%2B3=0, then ax%5E2%2Bbx=-3. So keep this fact in mind


p%28b-ap%29 Start with the left side of the second expression

=bp-ap%5E2 Distribute


Since we're assuming x+p is a factor, this means x=-p which means p=-x

=b%28-x%29-a%28-x%29%5E2 Plug in p=-x

=-bx-ax%5E2 Simplify


=-ax%5E2-bx Rearrange the terms


=-%28ax%5E2%2Bbx%29 Factor out a negative 1

Remember ax%5E2%2Bbx=-3, so let's substitute that in

=-%28-3%29 Replace ax%5E2%2Bbx with -3

=3 Negate -3 to get 3

So we've algebraically manipulated p%28b-ap%29 to get 3. So we've just shown that p%28b-ap%29 is equal to 3


So that means we've proven that p%28b-ap%29=3 is true.