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given-that-the-polynomial-p-x-3x-2-x-1-q-x-2x-4-of-degree-3-is-exactly-divisible-by-x-2-and-that-p-1-12-find-q-x-

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Question Number 97606 by hardylanes last updated on 08/Jun/20
given that the polynomial p(x)=(3x+2)(x−1)q(x)−2x−4 of degree 3 is exactly divisible by x−2 and that p(−1)=−12. find q(x).
giventhatthepolynomialp(x)=(3x+2)(x−1)q(x)−2x−4ofdegree3isexactlydivisiblebyx−2andthatp(−1)=−12.findq(x).
Answered by mr W last updated on 08/Jun/20
g(x)=ax+b p(−1)=(−3+2)(−1−1)g(−1)+2−4=−12 ⇒g(−1)=−5 ⇒−a+b=−5 ...(i) p(2)=(6+2)(2−1)g(2)−4−4=0 ⇒g(2)=1 ⇒2a+b=1 ...(ii) ⇒a=2 ⇒b=−3 ⇒g(x)=2x−3
g(x)=ax+bp(−1)=(−3+2)(−1−1)g(−1)+2−4=−12⇒g(−1)=−5⇒−a+b=−5…(i)p(2)=(6+2)(2−1)g(2)−4−4=0⇒g(2)=1⇒2a+b=1…(ii)⇒a=2⇒b=−3⇒g(x)=2x−3

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