Question

The polynomial px^3-x^2+qx-2 has no remainder when divided by (x-1) and a remainder of -18 when divided by (x+2). What are the values of p and q? Can you show steps please.

Answer 1

x

2

−2x−3=(x+1)(x−3)

x

3

−2x

2

+px−q−(x−6)=0 at x=−1 and x=3. (∵(x−6) is the remainder)

put x=−1,

−1−2−p−q+1+6=0

⇒p+q=4…eqn(1)

Now, put x=3

27−18+3p−q−3+6=0

⇒3p−q=−12…eqn(2)

Add equation 1 and 2, we get

4p=−8⇒p=−2

and q=4−p=6

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