Question

P(x) =2x3 -11x2 -4x +1 g(x) =2x +1

Answer 1

Answer:

see explanation

Step-by-step explanation:

If (2x + 1) is a factor then x = - $\frac{1}{2}$ is a root and P(- $\frac{1}{2}$ ) = 0 ← Factor theorem

P(- $\frac{1}{2}$ )

= 2(- $\frac{1}{2}$ )³ - 11(- $\frac{1}{2}$ )² - 4(- $\frac{1}{2}$ ) + 1

= - $\frac{1}{4}$ - $\frac{11}{4}$ + 2 + 1

= - $\frac{12}{4}$ + 3

= - 3 + 3

= 0

Since P(- $\frac{1}{2}$ ) = 0 then g(x) is a factor of P(x)