Question

remainder factor theorem of 2x3-9x2-11x+30​

Answer 1

Solution:-

${\huge{\underline{\small{\mathbb{\pink{p(x) \ = {2x}^{3} - 9 \ {x}^{2} -11 \ +30p}}}}}}$

${\huge{\underline{\small{\mathbb{\pink{(x) \ = \ 2x \ 3}}}}}}$

−9x 2

−11x+30

By trial we find that,

( - 2) = - 16 - 36 - 22 + 30

= - 52 + 52 = 0

p(−2)=−16−36−22+30

=−52+52=0

Therefore,

${\huge{\underline{\small{\mathbb{\pink{(x+y) \ is \ a \ factor(x+y) \ isafactor Divide p (x) with (x+2)}}}}}}$

We get :

${\huge{\underline{\small{\mathbb{\pink{2 {x}^2 \13x + 5 \ 2 x-10x - 3x + 15 2x(x-5)-3 (2x - 3) \ (x-5)}}}}}}$

2x 2 −13x+15

2x−10x−3x+15

2x(x−5)−3(x−5)

(2x−3)(x−5)

p(x) = (x + 2)(2x - 3)(x - 5)p(x)=(x+2)(2x−3)(x−5)

$\sf\red{Thank\:you!}$

$\bigstar \: \boxed{\sf{\color{Lime}{@ImmortalBarbie}}}$