Question

Use the factor theorem to determine if( x - 2) + (x + 4) are factors of the function below

Answer 1

Here, the dividend is x^3-6x^2+11x+6 and the divisor is x-2.

Put the value of divisor as 0 implies,

`\begin{gathered} x-2=0 \\ x=2 \end{gathered}`

Find f(2) implies,

`\begin{gathered} f(2)=2^3-(6*2^2)+(11*2)-6 \\ =8-24+22-6 \\ =0 \end{gathered}`

Therefore, x-2 is a factor of the polynomial.

Pu the value 0 for x+4 gives,

`\begin{gathered} x+4=0 \\ x=-4 \end{gathered}`

Find f(-4) gives,

`\begin{gathered} f(-4)=(-4)^3-(6*(-4)^2)+(11*-4)-6 \\ =-64-96-44-6 \\ =-210 \end{gathered}`

Therefore, x+4 is not a factor of polynomial.

Hence, Option C.