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Algebra
10.1 Adding and Subtracting Polynomials
Intro
• Polynomial-the sum of terms in the form axk where k is a nonnegative integer.
• A polynomial is usually written in standard form meaning the terms are placed in descending order by degree(exponent).
-4x3 + 5x2 – 4x + 9
Leading coefficient
The degree of a polynomial is the largest exponent.
This is a polynomial of degree 3.
12x – 8x2 + 6
Classifying Polynomials
Polynomial Degree # Degree Name Name by Numberof terms
6 0 constant monomial
-2x 1 linear monomial
3x + 1 1 linear binomial
-x2 + 2x – 5 2 quadratic trinomial
4x3 – 8x 3 cubic binomial
2x4 – 3x2 + 4x – 7 4 quartic polynomial
Terms Name 1 2 3 >3
Degree Name 0 1 2 3
Monomial Constant Binomial
TrinomialPolynomial
Linear Quadratic
Cubic
Writing a Polynomial in Standard Form
• Let’s try: 4x – 3x3 + 2x2 – 9
Standard form: -3x3 + 2x2 + 4x – 9
• You try: -9x + 3 + 4x2 – 10x4
Standard form: -10x4 + 4x2 – 9x + 3
What is the leading coefficient? -10
Classify this polynomial by degree.
Cubic
Adding Polynomials
Let’s try: (6x2 – x + 3) + (-2x + x2 – 7) + (4x + 2)
Answer: 7x2 - 2+ x
You try: (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3)
Answer: -11x3 - x+ 3x2 + 5
Classify this polynomial by the number of terms.
Trinomial
What is the leading coefficient? -11
Subtracting Polynomials
Let’s try: (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1)
(-6x3 + 5x – 3) + (-2x3 – 4x2 + 3x – 1)
Answer: -8x3 + 8x- 4x2
You try: (12x – 8x2 + 6) – (-8x2 – 3x + 4)
Answer: + 215x
- 4
(12x – 8x2 + 6) + (8x2 + 3x – 4)
Classify this polynomial by degree.
Linear
Classify this polynomial by the # of terms.
Binomial
HW
• P. 579 – 580 (13-29 odd, 53-60, 73-78)