Question

Use the factor theorem to determine whether g(x) =x+1 is a factor of p(x) in the following p(x) =2x^3+x^2 -2x -1​

Answer 1

Use the factor theorem to determine whether g(x) =x+1 is a factor of p(x) in the following p(x) =2x^3+x^2 -2x -1.

Answer 2

Given :-

• $\boxed{\sf{{p(x) =2 {x}^{3} + {x}^{2} - 2x - 1}}}$

To check:-

• Whether (x + 1 = 0) is a factor of p(x) or not.

Solution :-

$\mathsf{x = -1}$

• On placing the value of x if the equation leaves remainder 0 it means x+1 is a factor.

$\mathsf{\: \: \: \: \: \: \: \red{:\implies p(x) =2 {x}^{3} + {x}^{2} - 2x - 1}}$

$\mathsf{\: \: \: \: \: \: \: :\implies p(-1) =2 {(-1)}^{3} + {(-1)}^{2} - (-1 \times 2)- 1}$

$\mathsf{\: \: \: \: \: \: \: :\implies p(-1) = - 2 + 1 + 2 - 1}$

$\mathsf{\: \: \: \: \: \: \: :\implies p(-1) = - 1 + 1}$

$\mathsf{\: \: \: \: \: \: \:\red{ :\implies p(-1) = 0}}$

• Since, on placing x as -1 gives remainder 0 .That means, $\sf \purple{(x+1 )}$ is a factor of $\mathsf{ \purple{2 {x}^{3} + {x}^{2} - 2x - 1.}}$