1
5.6

• Dividing Polynomials

2
Dividing Polynomials

• Dividing a Polynomial by a Monomial
• Divide each term of the polynomial by the
  monomial.

Example
3
Dividing Polynomials

• Dividing a polynomial by a polynomial other than
  a monomial uses a long division technique that
  is similar to the process known as long division
  in dividing two numbers, which is reviewed on the
  next slide.

4
Dividing Polynomials
Divide 43 into 72.
Multiply 1 times 43.
Subtract 43 from 72.
Bring down 5.
Divide 43 into 295.
Multiply 6 times 43.
Subtract 258 from 295.
Bring down 6.
Divide 43 into 376.
Multiply 8 times 43.
Subtract 344 from 376.
Nothing to bring down.
5
Dividing Polynomials
As you can see from the previous example, there
is a pattern in the long division
technique. Divide. Multiply. Subtract. Bring
down. Then repeat these steps until you cant
bring down or divide any longer. We will
incorporate this same repeated technique with
dividing polynomials.
6
Dividing Polynomials Using Long Division
Example Divide
1. Divide the leading term of the dividend, c2,
by the first term of the divisor, x.
2. Multiply c by c 1.
3. Subtract c2 c from c2 3c 2.
Continued.
7
Dividing Polynomials Using Long Division
Example continued
Bring down the next term to obtain a new
polynomial.
4. Repeat the process until the degree of the
remainder is less than the degree of the binomial
divisor.
5. Check by verifying that (Quotient)(Divisor)
Remainder Dividend.
?
8
Dividing Polynomials
Divide 7x into 28x2.
Multiply 4x times 7x 3.
Subtract 28x2 12x from 28x2 23x.
Bring down 15.
Divide 7x into 35x.
Multiply 5 times 7x 3.
Subtract 35x 15 from 35x 15.
Nothing to bring down.
So our answer is 4x 5.
9
Dividing Polynomials
Divide 2x into 4x2.
Multiply 2x times 2x7.
Subtract 4x2 14x from 4x2 6x.
Bring down 8.
Divide 2x into 20x.
Multiply -10 times 2x7.
Subtract 20x70 from 20x8.
78
Nothing to bring down.