Answer:
There is no remainder. This means (3x+5) is a factor.
Step-by-step explanation:
We divide (3x+5) into the polynomial [tex]9x^3+18x^2+23x+30[/tex] through long division or synthetic. We choose long division and look for what will multiply with (3x+5) to make the polynomial [tex]9x^3+18x^2+23x+30[/tex] .
[tex](3x+5)(3x^2)=9x^3+15x^2[/tex]
We subtract this from the original [tex]9x^3-(9x^3)+18x^2-(15x^2)+23x+30[/tex].
This leaves [tex]3x^2+23x+30[/tex]. We repeat the step above.
[tex](3x+5)(x)=-3x^2+5x[/tex].
We subtract this from [tex]3x^2-(-3x^2)+23x-(5x)+30=18x+30[/tex]. We repeat the step above.
[tex](3x+5)(6)=18x+30[/tex].
We subtract this from [tex]18x-18x+30-30=0[/tex]. There is no remainder. This means (3x+5) is a factor.
