Question

factorize 2x^3+x^2-2n-1​

Answer 1

Explanation:

Let the polynomial be p(x).

By trial and error, we can see that p(-1)=0.

$p(-1)=2(-1)^3+(-1)^2-2(-1)-1=-2+1+2-1$

$p(-1)=0$

Hence according to the factor theorem, since p(-1) is equal to 0, (x+1) is a factor of p(x), for -1 is the zero for x+1.

$p(x)= 2x^3+x^2-2n-1$

$p(x)=2x^2(x+1)-x(x+1)-1(x+1)$

$p(x)=(x+1)(2x^2-x-1)$

$p(x)=(x+1)(2x^2 - 2x+x-1)$

$p(x)=(x+1)(x-1)(2x +1)$

Answer: (x+1)(x-1)(2x+1)