Consider the cubic polynomial

MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials

Problem

Consider the cubic polynomial q(x)=x3+px2+qx+12q(x)=x^{3}+px^{2}+qx+12. The remainder is 44 when q(x)q(x) is divided by (x−2)(x-2) and −23-23 when divided by (x+3)(x+3). What is the ordered pair (p,q)(p,q)? (a) (−5615,−3215)\left(-\dfrac{56}{15},-\dfrac{32}{15}\right) (b) (−1615,−8815)\left(-\dfrac{16}{15},-\dfrac{88}{15}\right) (c) (−3215,−5615)\left(-\dfrac{32}{15},-\dfrac{56}{15}\right) (d) (−3215,5615)\left(-\dfrac{32}{15},\dfrac{56}{15}\right)

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