Question

Using factor theorem,find if g(x) is a factor of p(x)

Answer 1

given that g(x) is a factor of p(x) . then ,
g(x) = 0
2x+1 = 0
2x = -1
x = -1/2

Now substitute this value in polynomial p(x) ,

p(-1/2) = 2 × (-1/2)^3 + (-1/2)^2 - 2(-1/2) - 1

p(-1/2) = 0


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Answer 2

Given p(x) = 2x^3 + x^2 - 2x - 1 and g(x) = 2x + 1.

Apply remainder theorem, we get

2x + 1 = 0

2x = -1

x = -1/2.

Substitute x = -1/2 in p(x), we get

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

           $= - \frac{1}{4} + \frac{1}{4} + 1 - 1$

          $= 0$



We got remainder as 0, therefore 2x + 1 is a factor of 2x^3 + x^2 - 2x - 1.


Hope this helps!