1. Section 2.4: Real Zeros of Polynomial Functions

2. Polynomial Long Division
Divide by w – 3. Divide by .

3. Synthetic Division
Divide by x – 1. Divide by x – 2.

4. Remainder Theorem
If dividing f(x) by x – a, f(a) will determine the remainder. What is the remainder when dividing by x – 4? Use the Remainder Theorem to evaluate f (x) = 6x3 – 5x2 + 4x – 17 at x = 3.

5. Factor Theorem
When dividing polynomials, if the remainder is zero, then the divisor is a factor. Use the Factor Theorem to determine whether x – 1 is a factor of f (x) = 2x4 + 3x2 – 5x + 7. Using the Factor Theorem, verify that x + 4 is a factor of f (x) = 5x4 + 16x3 – 15x2 + 8x + 16.

6. Finding Exact Irrational Zeros
Find the exact zeros for the function. Identify each zero as rational or irrational.

7. Writing Functions w/ Given Conditions
If the zeros of the function are -3, 7, and -1, and the leading coefficient is 4, write an equation for the function.

8. Rational Zeros Theorem
Given a function with constant of p and leading coefficient of q, all possible rational zeros can be found by Find the possible rational zeros of . Find the possible rational zeros of

9. Upper and Lower Bounds Test
When dividing polynomials, if the quotient polynomial has all non-negative coefficients, then the “k” value is an upper bound. If the quotient polynomial has alternating sign coefficients, then the “k” value is a lower bound. Show that all real roots of the equation lie between - 4 and 4.