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3 years ago

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?

Mathematics

1 answer:

rusak2 [61]3 years ago

4 0

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.

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