Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials.

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Presentation transcript:

Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials

Long Division Review

Synthetic Division Review | Since,, that means our first term is an x 3.

The Remainder Theorem  If a polynomial is divided by another polynomial and it equals the quotient with NO Remainder, then the divisor and the quotient are factors of the dividend. and are factors of

The Factor Theorem  A polynomial f(x) has a factor x – k, if and only if f(k) = 0.  Which means two things: 1.f(x) divided by x – k has no remainder. 2.k is a root (zero, x-intercept) of f(x).`

Using the Factor Theorem  Divide f(x) by x + 4 to find the remaining factor.  Also, -4 is a root of f(x). Solve given that

Solve given that f(-4)=0.

Solve given that f(-3)= |

You Try One! Solve given that Don’t Forget

Solve given that f(-1)=0 and f(1) = 0. Use Quadratic Formula to find the last two zeroes. The zeroes are –1, 1,.