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

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

Start with the left side of the second expression

= Distribute

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

= Plug in

= Simplify

= Rearrange the terms

= Factor out a negative 1

Remember , so let's substitute that in

= Replace with -3

= Negate -3 to get 3

So we've algebraically manipulated to get 3. So we've just shown that is equal to 3

So that means we've proven that is true.

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