If P(x) and Q(x) have a common factor (x-

Question

h),prove that (x-h) is also a factor of P(x)- Q
(x).find the possible common factors when P
(x)=ax^3 + x^2 - 15x - 18 and Q(x)= ax^3 - 14x -
12.also find the corresponding value of a.

Plz show me step of work

Answer 1

This just the same as showing that property with numbers.

If a|p and a|q then a|p-q

p = a*m and q=a*n
p-q = a(m-n) so a|p-q

for your polynomials,
P-Q = (ax^3+x^2-15x-18)-(ax^3-14x-12)
= x^2-x-6
= (x-3)(x+2)

that should get you going, right?

Answer 2

no sir plz i dont know it

Answer 3

huh? surely you recall the distributive property

(x-h) divides P(x), so P(x) = (x-h)*p(x)
similarly, Q(x) = (x-h)*q(x)

So, P-Q = (x-h)*p(x) - (x-h)*q(x)
= (x-h)(p(x)-q(x))
so, x-h divides P-Q

And above, I showed you what that is, and even factored it for you! So, those factors are the only possible common factors of P and Q.

As for finding a, you just need to find a so that those factors divide P and Q.

Answer 4

Sir please explain more.... help us in solving it more