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-

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