Divison and Rational Root Theorem: Reviewing Polynomial Division and Finding Roots

1. Division and Rational Root TheoremTS: Making decisions after reflection and reviewObj: Review polynomial division and how to find the roots of polynomials Find the cubic equation with zeros of -2, 1 and 5 and passes through the point (-1, 24) Warm-Up: Think back to Algebra 2, what we have done so far and what you know about zeros and points on a function and answer the following.

2. Two kinds of division: Long Division – When is it used? Synthetic Division – When is it used?

3. Synthetic Division vs. Long Division 1) (x7 + 1) ÷ (x + 1)

4. Synthetic Division vs. Long Division 2)(5x3 + 6x + 8) ÷ (x + 2)

5. Synthetic Division vs. Long Division 3) (4x4 + 8x) ÷ (x2 – 1)

6. The Remainder Theorem If a polynomial f(x)is divided by x – k, the remainer is r = f(k). Rational Root Theorem If the polynomial f(x) = anxn + an-1xn-1 + … + a2x2 + a1x + a0 Has integer coefficients, every rational zero of f has the form Rational zero = Where p and q have no common factors other than 1, p is a factor of the constant term a0 and q is a factor of the leading coefficient an

7. Given P(x) = x6 – 2x4 + x3 – 5x2 + 1 Find P(2)

8. Given f(x) = x3 – 2x2 +a x – 4 If f(2) = 4, what is a?

9. Factor x3 + 3x2 – 10x – 24

10. Find all the zeros of x5 – x4 – 3x3 + 5x2 - 2x = 0

11. Now You Try:1) Fully factor 8x4 – 14x3 – 71x2 – 10x + 24 (How do I check my solution with my calc I wonder???)2) What is the remainder of (x-3)(x-4)(x-1)4divided by x? Ans: 12