“You wasted $150,000 on an education you coulda got for $1

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5.5: Polynomial Long Division and Synthetic Division

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Presentation transcript:

“You wasted $150,000 on an education you coulda got for $1 “You wasted $150,000 on an education you coulda got for $1.50 in late fees at the public library.”

3.6 Real Zeros of a Polynomial Function

Synthetic Division Review Let’s review synthetic division: We can use synthetic division to help us completely factor polynomials.

Factoring Completely factor the following function: Hint: -1 is one zero of the function How can we find out what factor to start with when using synthetic division????

Rational Zeros Theorem Let f be a polynomial function of the form where each coefficient is an integer. If is a rational zero of f, then p must be a factor of , and q must be a factor of .

Potential Rational Zeros List the potential rational zeros of the following function:

Remainder Theorem Let f be a polynomial function. If f (x) is divided by x – c, then the remainder is f (c).

Potential Rational Zeros List the potential rational zeros of the following function. Then find the zeros and factor over the reals.

Real Zeros of Polynomials Find the real zeros of f and factor f over the reals.

Real Zeros of Polynomials Find the real zeros of f and factor f over the reals.

Practice Problem Find the real zeros of f and factor f over the reals.

3.6 Real Zeros of a Polynomial Function HW #9: p.231 #11 – 19 Odd 39, 41, 63, 69