SOLUTION: I need to find the quotient and remainder for (4x^3-5x^2+2x-6)/(x^2-3x). I know how to divide polynomials, but what is throwing me off is the (x^2-3x) part. Should I factor that ou

Question 640768: I need to find the quotient and remainder for (4x^3-5x^2+2x-6)/(x^2-3x). I know how to divide polynomials, but what is throwing me off is the (x^2-3x) part. Should I factor that out or can I just divide the first polynomial by that and solve? Do I need to instead divide by 0x^3+x^2-3x because the first polynomial has an exponent with a power of 3? It may just be easier if you would take me through it step by step instead. Thank you so much.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

I need to find the quotient and remainder for (4x^3-5x^2+2x-6)/(x^2-3x). I know how to divide polynomials, but what is throwing me off is the (x^2-3x) part. Should I factor that out or can I just divide the first polynomial by that and solve? Do I need to instead divide by 0x^3+x^2-3x because the first polynomial has an exponent with a power of 3? It may just be easier if you would take me through it step by step instead. Thank you so much.

You simply set this up as long-division of a polynomial, with as the dividend, and as the divisor. It's somewhat difficult to demonstrate it here.

I'll start you off though.

When you do the 1st division, the 1st of the quotient-expression is 4x, which when multiplied by gives you:

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