Polynomials Classifying, Adding, Subtracting, Multiplying Monomials in one variable The product of a constant and a variable raised to a nonnegative integer power. 2x4 2 is the coefficient degree 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: Coefficient 6x2 3x1/2 -(2) x3 4x-3 3 -5x
x4 Yes Yes 6 3 Degree 3 1 Like Terms
Two 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 = 7x4 2x4 - 5x4 = (2 - 5)x4 = -3x4 Polynomial: A monomial or the sum of monomials Terms are the monomials that make up the
polynomial. 2x2y one term monomial 2x2y + 5 two terms binomial 5x2 3x + 10 three terms trinomial 2x5 + 3x3 -6x + 9 four terms polynomial (or more) with 4 terms
Degree of a Polynomial The largest exponent of the polynomial is the degree if the polynomial has only one variable. 5x2 3x + 10 degree is 2 The coefficient of the term with the highest exponent is the leading coefficient. 5x2 3x + 10 leading coefficient is 5
Name the type of Polynomial. Coefficients 3x2 -5 Bi 3 9y3 2y2 + 3 3 Poly. 1/x Z 5 + (x2+1)/(x+5) 5x + 2 3
0 Degree 2 9 3 Zero Polynomial and Standard Form Zero 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 Polynomials Find the sum of (8x3 2x2 + 6x 2) and (3x4 2x3 + x2 + x).
Subtracting Polynomials Find the difference: (3x4 - 4x3 + 6x2 1) (2x4 - 8x2 - 6x +5) Multiplying Polynomials May use the distributive property, FOIL, or Box method Find the product: a. (x + 3)(x + 1) b. (2x + 1)(3x + 4)
Find the product: c. (2x + 5)(x2 - x + 2) 3x + 2) d. (x2 + 5x 4)(x2 Dividing Polynomials Find the quotient: a. 3x3 4x2 7x x
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