Given-that-the-expression-2x-3-px-2-8x-9-is-exactly-divisable-by-x-2-6x-5-find-the-value-of-p-and-q-Hence-factorise-the-expression-fully-

Question Number 85490 by oustmuchiya@gmail.com last updated on 22/Mar/20

G i v e n t h a t t h e e x p r e s s i o n 2 x^{3} + {p x}^{2} - 8 x + 9 i s e x a c t l y d i v i s a b l e b y x^{2} - 6 x + 5, f i n d t h e v a l u e o f p a n d q . H e n c e f a c t o r i s e t h e e x p r e s s i o n f u l l y

Commented by john santu last updated on 22/Mar/20

n o t h i n g q i n t h i s e q u a t i o n .

q u e s t i o n w r o n g!

Commented by john santu last updated on 22/Mar/20

i f d o y o u m e a n

2 x^{3} + {p x}^{2} - 8 x + q

b y r e m a i n d e r t h e o r e m

2 x (6 x - 5) + p (6 x - 5) - 8 x + q

12 x^{2} - 10 x + 6 p x - 5 p - 8 x + q

12 (6 x - 5) + 6 p x - 18 x - 5 p + q

72 x - 60 + 6 p x - 18 x - 5 p + q

(54 + 6 p) x + q - 5 p - 60 \equiv 0 x + 0

\Rightarrow 6 p = - 54 \Rightarrow p = - 9

\Rightarrow q = 60 + 5 p = 60 - 45 = 15

Commented by john santu last updated on 22/Mar/20

t h e n f a c t o r i s e

2 x^{3} - 9 x^{2} - 8 x + 15 = (x^{2} - 6 x + 5) (2 x + 3)