Question

State if the given binomial is a factor of the given polynomial (5n^3+13n^2+3n-1)÷(n-2)

Answer 1

The given polynomial is,

`f(n)=5n^3+13n^2+3n-1`

According to the factor theorem, x-a is factor of the polynomial f(x) only if f(a)=0.

Hence, n-2 is a factor of polyynomial f(n), then f(2) should be equal to zero.

So, first find f(2).

`\begin{gathered} f(2)=5*2^3+13*2^2+3*2-1 \\ =5*8+13*4^{}+3*2-1 \\ =40+52+6-1 \\ =97 \end{gathered}`

So,

`f(n)=97\\e0`

Therefore, x-2 is not a factor of the given polynomial