6.5 day 1 rational zeros theorem. if is in simplest form and is a rational root of the polynomial...

6.5 Day 1 Rational Zeros Theorem

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6.5 Day 1

Rational Zeros Theorem

If is in simplest form and is a rational root of the polynomial equation

With integer coefficients, then p must be a factor of and q must be a factor of

0... 011

1 axaxaxa nn

0a na

Page 3: 6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a

Tominaga Version

p is a factor of the constant, q is a factor of the leading coefficient. The list of all p/q is the list of all POSSIBLE RATIONAL ROOTS.

Page 4: 6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a

Example: Find all the possible rational zeros for the function.

02425 23 xxx

Page 5: 6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a

Testing using synthetic division to find a zero

• Find all of the p’s

• Find all of the q’s

• Make a list of p/q

• Use synthetic division to determine if the number tested is a zero (if you get 0 for a remainder, you have a root)

Page 6: 6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a

Find all rational zeros for the function.

02425 23 xxx

Page 7: 6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a

Find all rational zeros for the function.

0824 23 xxx

Page 8: 6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a

Find all zeros for the function.

013 23 xxx

Page 9: 6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a

Homework

1/30: #7 pg 339 1-12 all

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