Review of Polynomials

Classifying

•A monomial is an expression with a single term. It is a real number, a variable, or the product of real numbers and variables.

•For example, 4 , 3x 2 and 15xy 3 are all monomials.

Classifying

•The degree of a polynomial is the largest of the degrees of its monomial terms.

•A polynomial can be arranged in ascending order.

•The polynomial3 + 12x - xy + 7x 2 y + y 5 -12x 3 y 3 is written in ascending order as -12x 3 y 3 + y 5 +7x 2 y - xy + 12x + 3 is written in descending order.

Classifying - Examples

1) 2p4 + p3

2) -10a3) 2x2

Answers:

4) # of terms: 2, degree: 45) # of terms: 1, degree: 16) # of terms: 1, degree: 2

Adding & Subtracting

•Simplify (2x + 5y) + (3x – 2y) • I'll clear the parentheses, group like

terms, and then simplify:•(2x + 5y) + (3x – 2y)

  =  2x + 5y + 3x – 2y   =  2x + 3x + 5y – 2y   =  5x + 3y

Adding & Subtracting• Simplify (3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x –

4) • Horizontally(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)

  =  3x3 + 3x2 – 4x + 5 + x3 – 2x2 + x – 4   =  3x3 + x3 + 3x2 – 2x2 – 4x + x + 5 – 4   =  4x3 + 1x2 – 3x + 1

• Vertically3x3 + 3x2 – 4x + 5+x3 – 2x2 + x - 44x3 + 1x2 - 3x + 1

Either way you getthe same answer

Multiplying

•(3x – 5)(5x + 2)

3x -5

5x

+2

Multiplying

3x -5

5x 15x2 -25x

+2 6x -10

Combine like terms to write your answer.

15x2 – 19x - 10