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

Answer:

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

Step-by-step 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.