Question

What is the result when 9 x 3 + 18 x 2 + 23 x + 30 9x 3 +18x 2 +23x+30 is divided by 3 x + 5 3x+5?

Answer 1

There is no remainder. This means (3x+5) is a factor.

Explanation:

We divide (3x+5) into the polynomial
`9x^3+18x^2+23x+30` through long division or synthetic. We choose long division and look for what will multiply with (3x+5) to make the polynomial
`9x^3+18x^2+23x+30` .

`(3x+5)(3x^2)=9x^3+15x^2`

We subtract this from the original
`9x^3-(9x^3)+18x^2-(15x^2)+23x+30`.

This leaves
`3x^2+23x+30`. We repeat the step above.

`(3x+5)(x)=-3x^2+5x`.

We subtract this from
`3x^2-(-3x^2)+23x-(5x)+30=18x+30`. We repeat the step above.

`(3x+5)(6)=18x+30`.

We subtract this from
`18x-18x+30-30=0`. There is no remainder. This means (3x+5) is a factor.