Question

Find the values of p and q if the polynomial x^3 + px^2 + 4x + 5 has X - 1 as a factor and leaves
remainder 3 when divided by X-2​

Answer 1

Answer:

Remainder theorem:

When we divide f(x) by (x−c) , the remainder f(c)

When p(x)=4x^3 −2x^2+px+5 is divided by (x+2), the remainder is

p(−2)=4(−2)^3−2(−2)^2 +p(−2)+5

=−2p−35

So,

a=−2p−35

When q(x)=x^3+6x 2+p is divided by (x+2), the remainder is

q(−2)=(−2)^3+6(−2)^2+p

=p+16

So,

b=p+16

Now

a+b=0

−2p−35+p+16=0

−p−19=0

p=−19

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