Unit 3A: Polynomials, Part 2

2017

pebblebrook high schoolALGBRA 2

3A.1 – 3A.5

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

Synthetic Division: Let’s watch a video…https://youtu.be/1byR9UEQJN0

Example #2: Divide using synthetic division

You try: Divide using both methods

Section 3A.2 Remainder Root Theorem

Purpose – find values to the output of the function, P(x).

Example #1: 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

3A.3 Rational Root Theorem

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 ca

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….

Section 3A.4 Irrational Root Theorem

Example #1: Finding Irrational Roots1) 1 + √3

2) –√11

Examples #2: Finding Imaginary Roots1) 3 – i

2) 2i

You Try….

3A.5 Writing the Equation of a Polynomial

Example #1: Write the polynomial in standard given the zeros.

1) x = -2, 3, 3

2) x = 0, 2, -4

3) x = -1, 23 , 5

Example #2: Write the polynomial in standard form given the complex roots.

1) x = 2i

2) x = 6i

3) x = -1, 3i

4) x = 3, 4i

You Try…SHOW WORK!!!!