Polynomials Classifying Adding Subtracting Multiplying Monomials in one

Polynomials Classifying, Adding, Subtracting, Multiplying

Monomials in one variable �The product of a constant and a variable raised to a nonnegative integer power. � 2 x 4 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 � 6 x 2 � 3 x 1/2 �-√(2) x 3 � 4 x-3 � 3 �-5 x �x 4 Yes Degree 6 Yes 3 3 1½

Like Terms �Two monomials with the same variable raised to the same power. � 2 x 4 and -5 x 4 are like terms �Add or subtract like terms using the distributive property. � 2 x 4 + 5 x 4 = (2 + 5)x 4 = 7 x 4 � 2 x 4 - 5 x 4 = (2 - 5)x 4 = -3 x 4

Polynomial: �A monomial or the sum of monomials �Terms are the monomials that make up the polynomial. 2 x 2 y one term monomial 2 x 2 y + 5 two terms binomial 5 x 2 – 3 x + 10 three terms trinomial 2 x 5 + 3 x 3 -6 x + 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. � 5 x 2 – 3 x + 10 degree is 2 �The coefficient of the term with the highest exponent is the leading coefficient. � 5 x 2 – 3 x + 10 leading coefficient is 5

Name the type of Polynomial. � 3 x 2 -5 � 9 y 3 – 2 y 2 + 3 – 3 3 � 1/x �Z 5 + π �(x 2+1)/(x+5) � 5 x + √ 2 � 3 � 0 Coefficients Degree 3 2 Bi Poly. 9

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. � 2 x 5 + 4 x 4 – 3 x 3 – 2 x 2+ 6 x + 9

Adding Polynomials �Find the sum of (8 x 3 – 2 x 2 + 6 x – 2) and (3 x 4 – 2 x 3 + x 2 + x).

Subtracting Polynomials �Find the difference: (3 x 4 - 4 x 3 + 6 x 2 – 1) – (2 x 4 - 8 x 2 - 6 x +5)

Multiplying Polynomials �May use the distributive property, FOIL, or Box method… �Find the product: a. (x + 3)(x + 1) b. (2 x + 1)(3 x + 4) �Find the product: c. (2 x + 5)(x 2 - x + 2) 2) d. (x 2 + 5 x – 4)(x 2 – 3 x +

Dividing Polynomials �Find the quotient: a. 3 x 3 – 4 x 2 – 7 x 16 x a. Answer: 3 x 2 – 4 x - 7 b. 4 x 4 – 8 x 3 – 2 x 2 2 x