Dividing Polynomials Two options: Long Division Synthetic Division.

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Presentation transcript:

Polynomial Division and Using Division to Solve More Difficult Polynomials

Dividing Polynomials Two options: Long Division Synthetic Division

Long Division Divide 134 by 5 using long division.

Polynomial Long Division Find the quotient and the remainder of

Polynomial Long Division Find the quotient and the remainder of

Let’s try the same example with Synthetic Division Find the quotient and the remainder of using synthetic division

Synthetic Division Find the quotient and the remainder of

Remainder Theorem If a polynomial is divided by x – a, then the remainder = f(a) Example: Find f(-2)

Factor Theorem x – a is a factor of f(x) only if the remainder is zero (or f(a) = 0) Example: Show that x – 2 and x + 3 area factors of

Using Division to Solve Polynomials Use synthetic division to show that x +4 is a factor of . Then, factor the polynomial completely.

Using Division to Solve Polynomials The polynomial has 3 zeros. If x = -3 is one of the zeros, find the remaining two roots.

Rational Roots (Zeros) Test Every rational zero that is possible for a given polynomial can be expressed as the factors of the constant term divided by the factors of the leading coefficient.

Solving Using the Rational Root Test List all possible rational roots for the polynomial y = 10x³ - 15x² - 16x + 12. Then, divide out the factor and solve for all remaining zeros.

Rational Roots Test List all possible rational roots for the polynomial y = x³ - 7x – 6. Then, divide out the factor and solve for all remaining zeros.

Practice Pg. 61 (1 – 13 odd, 19, 21) Pg. 84 (21, 22)