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