Intro to Polynomials

Polynomials A monomial is the product of numbers, variables, or both. Ex. 5 x 6y 7jk2 A polynomial is a monomial or a group of monomials separated by + or –. Ex. 7x2 + 8xk - 4

What does each prefix mean? mono bi tri

Naming a polynomial by Terms Number of Terms Name 1 Monomial 2 Binomial 3 Trinomial 4 or more “with 4 terms” (or 5 or 6, etc.)

State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x3yz2 monomial 3) not a polynomial

The degree of a monomial is the sum of the exponents of the variables The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x2 2 4a4b3c 8 -3

To find the degree of a polynomial, use the monomial with the highest degree. 1) 8x2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2 is the degree! 2) y7 + 6y4 + 3x4m4 Degrees: 7 4 8 8 is the degree!

Find the degree of x5 – x3y2 + 4 2 3 5 10

Sometimes, a polynomial will already be factored Sometimes, a polynomial will already be factored. When this is the case, add up all the exponents. Ex. (x-2)3(x+5)2(x-3)(x+7)(x+1)3

Quick Recap To find the degree of a polynomial, use the monomial with the largest degree. 7x3y + 9x2 + 4x + 5y If the polynomial is already factored, add up the exponents. (x-3)(x+4)(x-7) 3

Naming Polynomials by Degree Name Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 5 Quintic 6+ (nth degree) Naming Polynomials by Degree

Try it! Name the following polynomials: x3 x5 – xy + 3y2 t2 – 8 j4 + 6jk – 3j + 2

Adding and Subtracting Polynomials Combine like terms. Watch out for degrees! Don’t combine x and x2. When subtracting, be sure to distribute the negative to all terms.

Example 1: Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a)

Example 2: Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2)

Example 3: Add the following polynomials: (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2)

Example 4: Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)

Example 5: Subtract the following polynomials: (7a - 10b) - (3a + 4b)

Example 6: Subtract the following polynomials: (4x2 - 2xy + 3y2) - (-3x2 - xy + 2y2)

Find the sum or difference. (5a – 3b) + (2a + 6b)

Find the sum or difference. (5a – 3b) – (2a + 6b)