Unit 3A: Polynomials, Part 2
2017
pebblebrook high schoolALGBRA 2
3A.1 – 3A.3
3A.1 Dividing Polynomials
Recall how to do long division:
Let’s see to divide with polynomials using long division
https://youtu.be/H94ma2ofGuc
Let’s try: (5x2 + 3x – 2) ÷ (x + 1)
Example #1: Divide polynomials using long division
1)
Synthetic Division: Let’s watch a video…https://youtu.be/1byR9UEQJN0 Example #2: Divide using synthetic division
You try: Divide using both methods
Purpose – find values to the output of the function, P(x).
Example #3: Evaluate the polynomial using Synthetic Division
You Try…
FACTS: If P(a) = 0, the x – a is linear factor of the polynomial.
Example #4: Determine which is a factor of
a) x + 1 b) x + 2 c) x + 3 d) x – 3
Section 3A.1 Homework
3A.2 Theorems of Polynomials
Steps for finding rational roots:
1st- identify ALL factors a (coefficient of leading term of the polynomial
2nd – identify ALL factors of c (constant of polynomial)
3rd – find ALL answers to ac
4th – Plug the possible solutions into the original problem to see if the solution = 0.
Example #1: Find the rational roots.1) x3 + x2 – 3x – 3 = 0
2) 2x2 – x2 + 2x – 1 = 0
You Try….
Example #2: Finding Irrational Roots1) 1 + √3
2) –√11
Examples #3: Finding Imaginary Roots1) 3 – i
2) 2i
You Try….
Section 3A.2 Homework
3A.3 Roots of a polynomialsRoots ↔ Solutions↔ Zeros (x – values when y = 0)
Example #1: Find the zeros when in factored form.
1) Y = (x – 2) (x + 1) ( x – 3)
You Try…
Example #2: Find the zeros by factoring
You Try….
Example #3: Solve the polynomial
You Try….
Example #3: Write the polynomial in standard given the zeros.
1) x = -2, 3, 3
2) x = -1, 3i
You Try…
Section 3A.3 Homework
3) 1, -2i