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).

$\begin{gathered} f(2)=5\times2^3+13\times2^2+3\times2-1 \\ =5\times8+13\times4^{}+3\times2-1 \\ =40+52+6-1 \\ =97 \end{gathered}$

So,

$f(n)=97\ne0$

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