ADD AND SUBTRACT POLYNOMIALSChapter 9 section 1

Polynomials

15x – x3 + 3

Is a polynomial

A polynomial is a monomial or a sum of monomials, each called a term of the polynomial.

A polynomial can be named by its terms or its degree.

• A one term polynomial is called a monomial.• A monomial is a number, a variable, or the product of a

number and one or more variables with whole number exponents.

• A two term polynomial is called a binomial.• A binomial is the sum or difference of two binomials.

• A three term polynomial is called a trinomial.• A trinomial is the sum or difference of three binomials

• More than three terms is just called a polynomial.

Degree of a Polynomial

The degree of a polynomial is the greatest degree of its terms.

Leading coefficient

2x3 + x2 – 5x + 12

Degree Constant term

When a polynomial is written so that the exponents of a variable decrease from left to right.

Terms and Degrees

Is it a polynomial?

Classify by degree and number of terms.

• 15x – x3 + 3• 9• 2x2 + x – 5• 6n4 – 8n• n-2 – 3• 7bc3 + 4b4c

Addition and Subtraction• Addition• Combine like terms• (2x3 – 5x2 + x) + ( 2x2 + x3 –1)• (3x2 + x – 6) + (x2 + 4x + 10)

• Subtraction• Add the opposite• Combine like terms• (4n2 + 5) – (-2n2 + 2n – 4)• (4x2 – 3x + 5) – (3x2 – x – 8)

MULTIPLY AND DIVIDE POLYNOMIALSChapter 9 section 2

Multiplying a monomial by a polynomial

• Use the distributive property.• 2x3 (x3 + 3x2 – 2x + 5)

• x (7x2 + 4)

• 3x2 (2x3 – x2 + 4x – 3)

Multiplying a binomial by a binomial• FOIL• First times first• Outer times outer• Inner times inner• Last times last

(x – 4) (3x + 2)

Multiplying a binomial by a binomial• (3a + 4) ( a – 2)

• (4n – 1) (n + 5)

Multiplying a binomial by a trinomial

Use the box method• (2x2 + 5x – 1) (4x – 3)

• Combine like terms

2x2 5x -1

4x

-3

Multiplying Polynomials• (x2 + 2x + 1) (x + 2)

• (3y2 – y + 5) (2y – 3)

• (2x2 – x -2) (3x – 1)

Homework• Pages 557 – 558

#11-25 odd, • Pages 565 – 566

#23 - 39 odd