Question

Is x+4 a factor of `2x^3+3x^2-29x-60`?

Answer 1

`(x+4)` is not a factor of `f(x)=2x^3+3x^2-29x-60`

Explanation:

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

Here we have to test for `(x+4)` i.e. `(x-(-4))`. Therefore, if `f(-4)=0` then `(x+4)` is a factor of `f(x)=2x^3+3x^2-29x-60`.

`f(-4)=2(-4)^3+3(-4)^2-29(-4)-60`

= `2×(-64)+3×16-29×(-4)-60`

= `-128+48+116-60`

= `164-188=-24`

Hence `(x+4)` is not a factor of `f(x)=2x^3+3x^2-29x-60`.