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

$g i v e n t h a t t h e p o l y n o m i a l p (x) = (3 x + 2) (x - 1) q (x) - 2 x - 4$ $o f d e g r e e 3 i s e x a c t l y d i v i s i b l e b y x - 2 a n d$ $t h a t p (- 1) = - 12 . f i n d q (x) .$
	Answered by mr W last updated on 08/Jun/20

	$g (x) = a x + b$ $p (- 1) = (- 3 + 2) (- 1 - 1) g (- 1) + 2 - 4 = - 12$ $\Rightarrow g (- 1) = - 5$ $\Rightarrow - a + b = - 5 . . . (i)$ $p (2) = (6 + 2) (2 - 1) g (2) - 4 - 4 = 0$ $\Rightarrow g (2) = 1$ $\Rightarrow 2 a + b = 1 . . . (i i)$ $\Rightarrow a = 2$ $\Rightarrow b = - 3$ $\Rightarrow g (x) = 2 x - 3$
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