Question

use the factor theorem to determine whether g(x) is a factor of p(x) in each of a following cases (1.) p(x)=2x^3+x^2 -2x-1,g(x)=x+1 . please answer as soon as possible ​

Answer 1

Step-by-step explanation:

p(x)= 2x³+x²-2x-1

g(x)= x+1

If x+1=0

Then, x= -1

So, p(-1) = 2×(-1)³+(-1)²-2×(-1) - 1

= -2+1+2-1

= 0

Hence , g(x) is a factor of p(x) .

Answer 2

Answer:

$\large\boxed{\star\:\:Yes,\:(x+1)\:is\:a\:Factor\:of\:2x^3+x^2-2x-1.\:\:\star}$

Step-by-step explanation:

✵ Given:-

2x³+x²-2x-1=0 is a polynomial.

✵ To Check:-

   Whether (x+1) is a factor of 2x³+x²-2x-1=0.

✵ Solution:-

→ g(x)=x+1=0

→ x+1=0

→ x=(-1)

p(x)=2x³+x²-2x-1=0

Putting x=(-1):-

p(-1)=2(-1)³+(-1)²-2(-1)-1=0

⇒[2×(-1)]+1+2-1=0

⇒3-3=0

⇒0=0

LHS=RHS

∴ (x+1) is a Factor of polynomial 2x³+x²-2x-1.