Warm Up 9/2

• What is the remainder of ?

• Is x-1 a factor of the polynomial

Homework Questions

Announcements

• Quiz Friday

• HW 2.4 pg. 206 #’s 34-44 even, 50-56 even

Rational Zeros Theorem

• To find all possible rational roots, divide all the factors of the constant by all the factors of the leading coefficient.

Example

• Find the rational zeros for

Practice

• Find the rational zeros for f(x)=

Upper and Lower Bounds

• Upper Bound – If every number in last line of synthetic division is positive

• Lower Bound – If the numbers in last line of synthetic division alternate between positive and negative.

Example

• Prove that all the real zeros of f(x) = must lie in the interval [-2, 5]

Practice

• Prove that 3 is an upper bound for

• Prove that -1 is a lower bound for

Irrational Roots

• Find all real zeros of and tell which are rational and irrational

Practice

• Find all real zeros of and tell which are rational and irrational

Homework

• Section 2.4 pg. 206 #’s 34-44 even, 50-56 even

• Answers posted on website