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Presentation transcript:

Homework Questions?

Essential Question: How do I use synthetic division to find all of the zeros? What is synthetic division? How do I find all the solutions given 1 root?

Do you remember how to use Synthetic Division??!

Use Synthetic Division to divide x4 – 10x2 – 2x + 4 by (x + 3) -3 1 -10 -2 4 -3 9 3 -3 1 -3 -1 1 1 remainder

You Try!!

Factors vs. Roots Factors: What multiplies together to get the polynomial. The things in ( ) ex., (x+2), (2x-3), (x-8) Roots: What the x values equal. After setting the factor =0. Can also be called zeros, or solutions. ex., x=-2, x=3/2, x=8

Factor Theorem If remainder = 0 when we plug a #, root, into some function, then (x – #) is a factor.

Before… We could get a remainder using long division or synthetic division The last number using synthetic division is your remainder! We want a remainder of 0 to find the other roots…and we want to be able to find other roots!

Chapters 1 & 2 The Conservative Tradition in Educational Thought Determine whether (x + 2) is a factor of f(x) = 3x3 - x2 + 2x - 4 NO Answer:

You Try!! Determine whether (x - 6) is a factor of f(x) = x4 - 6x3 - 4x + 24

Can you use synthetic division when you divide by 3x-2?

Let’s Put It All Together!!

Chapters 1 & 2 The Conservative Tradition in Educational Thought If (x-1) is a factor, find the other factors of g(x) = 3x3 + 8x2 – 3x – 8 1 3 8 -3 -8 3 11 8 3 11 8 3x2 +11x +8 FACTOR! FACTORS:

(x-2) is a factor (x+3) is a factor Given that (x-2) and (x+3) are factors of and find the remaining factors. 2 2 7 -4 -27 -18 4 22 36 18 (x-2) is a factor -3 2 11 18 9 -6 -15 -9 (x+3) is a factor 2 5 3

You Try!! Given that (x-10) is a factor of , find the other factors. What are the roots?

HOMEWORK! Day 1C.1 Homework #1-10