5.3 Division of Polynomials. Dividing a Polynomial by a monomial.  Divide each term of the polynomial by the monomial.

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Presentation transcript:

5.3 Division of Polynomials

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

Dividing a Polynomial by a monomial.  Page 307  9  14  19

Dividing a polynomial by a binomial  Long Division vs. Synthetic Division

Long Division vs. Synthetic Division  A few examples.  Page 307  25  36  45

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.

What to watch for…..  Synthetic division sign errors  Not having the polynomials in descending order.  Forgetting all powers must be represented

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

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).

The Remainder Theorem  If the remainder is zero…… The binomial is a factor of the polynomial

The Remainder Theorem  Page 308 / 65, 66, 67