Division of Polynomials

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5.3

• Division of Polynomials

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Dividing a Polynomial by a monomial.

• Divide each term of the polynomial by the
  monomial.

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Dividing a Polynomial by a monomial.
Examples

• Page 307
• 9
• 14
• 19

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Dividing a polynomial by a binomial

• Long Division vs. Synthetic Division

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Long Division vs. Synthetic Division

• A few examples.
• Page 307
• 25
• 36
• 45

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When to use long division

• Page 307/ 28, 33, 46
• Leading coefficient is not 1
• When the degree of the divisor is higher than 1.

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What to watch for..

• Synthetic division sign errors
• Not having the polynomials in descending order.
• Forgetting all powers must be represented

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The Remainder Theorem

• Used to find if a polynomial is divisible by a
  binomial.
• To find the remainder.
• Is a binomial a factor of a polynomial

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The Remainder Theorem

• Evaluate the polynomial that you are dividing
  into with the opposite of the constant in the
  divisor.
• If p(x) is divided by x a, then the remainder
  is equal to p(a).

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The Remainder Theorem

• If the remainder is zero
• The binomial is a factor of the polynomial

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The Remainder Theorem
Examples

• Page 308 / 65, 66 , 67

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