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Unit 5.4 Polynomial Division

Polynomial Divided by a Monomial

When you have a polynomial divided by a monomial, you can break apart the polynomial and divide each term by the monomial. Make sure to divide each term

Polynomial divided by a monomial

Polynomial Divided by a Polynomial

When you have a polynomial divided by a polynomial, you have to use long division

Long Division: Polynomials

Put the dividend into the division house and put the divisor outside. You can only do this if the dividend is of a higher order than the divisor

We are looking ONLY at x and the highest value. What do you have to multiply x by to get x2 ? You need to multiply by x to turn x into x2. Then you multiply x by each of the divisor’s terms

In this example you get x2 + 2x. Since we multiplied by x, write that value on top

Subtract the value you obtained from the dividend, x2 – x2 = 0 and 4x – 2x = 2x.

We still need to deal with the 7. Drop it down to the new value

Again, only dealing with x and the next highest value. What do you have to multiply x by to get 2x? The answer is 2. Multiply 2 by each of the divisors terms and write that value on top. It is a positive 2 so we add 2

Subtract the obtained value. Because x does not go into 3 at all, you are finished

Your answer is x + 2 with a remainder of 3

 

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