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Unit 2 - Objective 3 - Division of Polynomials


You may need to review Unit 1 - Objective 4 - Rules of Exponents again. Remember (am) / (an) = am - n.

(In #1 the denominator should have x raised to the 2nd power)

Examples:

u2obu3-1.gif (4093 bytes)

To divide a polynomial by a mononomial, divide each term of the polynomial by the mononomial.

Examples:

1. u2obj3-6.gif (1388 bytes)

2. u2obj3-7.gif (1940 bytes)

NOTE: (#2 has some mistakes - numerator of the 1st line should be 3xy not 6xy

2nd line the numerator of the first term should be 3xy not 6xy

3rd line the first term should be 1 not 3 and the second term constant should be 4/3 not 4

4th line the first term should be 1 not 3 and the second term should be (4/3)y not 4y

To divide a polynomial by a polynomial follow these steps:

  1. Write both the dividend and the divisor in decreasing order of powers.
  2. Are there any missing terms? If there are then write a coefficient of 0.
  3. Set up the problem as long division.
  4. Divide the first term in the dividend by the first term in the divisor.
  5. Multiply the divisor by this first term of the quotient. Write the product below the dividend with like terms under like terms. Subtract the product from the dividend.
  6. Repeat the last two steps until the power of the new dividend is less than the power of the divisor.

Examples:

1. Divide 6x2 - 4 - 4x + 8x4 by 2x + 1

This first term in the dividend is 8x4 and the first term in the divisor is 2x. You would say 2x times what would give you 8x4 and you answer would be 4x3.


2. Divide 4x5 - 2x3 + 6x2 - 8 by (4x2 + 2)






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