Question

If a polynomial 2x^3+ax^2+7x-6 is exactly divisible by 2x-1. then find the value of a. hence factorise the polynomial

Answer 1

GIVEN : Let Polynomial f(x)=2x³+ax²+11x+a+3 …….(1)

Polynomial is exactly divisible by 2x-1 if the remainder is 0.

2x -1= 0

2x = 1

x = ½

By remainder theorem, when f(x) is divided by (2x-1) then remainder = f(½)

On Putting x= ½ in eq 1

f(1/2)=2(1/2)³+a(1/2)²+11(1/2)+a+3

0 =2(⅛)+a/4+11/2+a+3

0 = ¼+a/4+11/2+a+3

0 = ¼ + 11/2 +3 +a/4 +a

0 = (1+22+12)/4 +(a + 4a)/4

0= 35/4 + 5a/4

-35/4 = 5a/4

-35 = 5a

a = -35/5

a = -7

Hence, the value of a is -7

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