Polynomials

Classifying, Adding, Subtracting, MultiplyingPolynomialsMonomials in one variableThe product of a constant and a variable raised to a nonnegative integer power.

2x42 is the coefficientdegree is 4

What does it mean to be raised to a nonnegative integer power?

The degree of a monomial is found by adding the exponents together!Monomials:CoefficientDegree6x2Yes 6 33x1/2 Yes 3 1 -(2) x34x-33-5xx4Like TermsTwo monomials with the same variable raised to the same power.

2x4 and -5x4 are like terms

Add or subtract like terms using the distributive property.2x4 + 5x4 = (2 + 5)x4 = 7x42x4 - 5x4 = (2 - 5)x4 = -3x4

Polynomial:A monomial or the sum of monomials

Terms are the monomials that make up the polynomial.2x2yone term monomial2x2y + 5two termsbinomial5x2 3x + 10 three termstrinomial2x5 + 3x3 -6x + 9four termspolynomial (or more) with 4 termsDegree of a PolynomialThe largest exponent of the polynomial is the degree if the polynomial has only one variable.5x2 3x + 10degree is 2

The coefficient of the term with the highest exponent is the leading coefficient.5x2 3x + 10leading coefficient is 5

Name the type of Polynomial.CoefficientsDegree3x2 -5Bi 3 29y3 2y2 + 3 3 Poly. 9 31/xZ5 + (x2+1)/(x+5)5x + 230Zero Polynomial and Standard FormZero Polynomial: If all the coefficients are zero, the polynomial is called the zero polynomial.

Standard form: Polynomials are usually written in standard form, beginning with the nonzero term of highest degree and continuing with terms in descending order according to degree.2x5 + 4x4 3x3 2x2+ 6x + 9

Adding PolynomialsFind the sum of (8x3 2x2 + 6x 2) and (3x4 2x3 + x2 + x).

Subtracting PolynomialsFind the difference:(3x4 - 4x3 + 6x2 1) (2x4 - 8x2 - 6x +5)Multiplying PolynomialsMay use the distributive property, FOIL, or Box methodFind the product:a. (x + 3)(x + 1) b. (2x + 1)(3x + 4)

Find the product:c. (2x + 5)(x2 - x + 2) d. (x2 + 5x 4)(x2 3x + 2)Dividing PolynomialsFind the quotient:a. 3x3 4x2 7xb. 4x4 8x3 2x2 - 16 x 2x

a. Answer: 3x2 4x - 7