5-2:Dividing 5-2:Dividing Polynomials Polynomials

5-2:Dividing 5-2:Dividing Polynomials Polynomials

Unit 5: PolynomialsUnit 5: PolynomialsEnglish CasbarroEnglish Casbarro

Recall that you have been dividing numbers for a long time. Now we will be dividing polynomials.

When you checked your answer: Numerical: 21(32) = 672 Since there is a remainder of 0, they are factors of 672.Polynomial: (2x + 1)(3x + 2) = 6x2 + 7x + 2 Since there is a remainder of 0,They are factors of 6x2 + 7x + 2.

2 ways to divide polynomials

Long Division– works with every polynomial no changes to divisor

Synthetic Division– works easily only when the divisor is a binomial with a leading coefficient of 1 (i.e., looks like these: x + 3, x – 5, etc.). All others require some changes.

Remember numerical long division. You did not have a remainder in the first example, so you didn’t have to know how to write it. The answer was a factor of the polynomial. (which meansit was a root, or solution– remember quadratics?) Most of the time, it is NOTa root (although it will still give you the “y” coordinate of the point). Look again at the old way to do division:

Now, the first way you were taught to write the remainder was to leave it where it was.The second way you were taught to write the remainder:________ R _____

The third way you were taught was to make a fraction, and put it beside the number: 4/31

6855 31

6x3+ 8x2 + 5x + 5 3x + 1

You should always write your remainder in the form you see here.

It is usually written as 4x + 3 -

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