given the 3^(rd) degree polynomial P(x) = (2x −1)(x−3)Q(x) + 12x−8 given that (x−1) is a factor of P(x) and P(0) = 10 find Q(x)


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Question Number 73530 by Rio Michael last updated on 13/Nov/19

$g i v e n t h e 3^{r d} d e g r e e p o l y n o m i a l$ $P (x) = (2 x - 1) (x - 3) Q (x) + 12 x - 8$ $g i v e n t h a t (x - 1) i s a f a c t o r o f P (x) a n d P (0) = 10$ $f i n d Q (x)$
	Answered by MJS last updated on 13/Nov/19

	$y = (2 x - 1) (x - 3) (a x + b) + 12 x - 8$ $x = 0$ $10 = (- 1) (- 3) b - 8 \Rightarrow b = 6$ $(2 x - 1) (x - 3) (a x + 6) + 12 x - 8$ $(x - 1) is a factor \Rightarrow y = 0 for x = 1$ $0 = (1) (- 2) (a + 6) + 12 - 8 \Rightarrow a = - 4$ $Q (x) = (- 4 x + 6)$ $please check as I^{'} m in a hurry$
	Commented by Rio Michael last updated on 13/Nov/19

	$o k a y s i r t h a n k s i^{'} l l c h e c k$
	Commented by Rio Michael last updated on 13/Nov/19

	$c o r r e c t s i r t h a n k s$
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