Unit 1: Rational Numbers Test

Wednesday September 26th

Unit 2: Powers and Polynomials

Goals: - Represent polynomials geometrically - Simplify polynomial expressions using exponent laws - Add and subtract polynomials - Multiply a polynomial by a monomial

Terminology

• Algebraic expression - a mathematical phrase made up of numbers and variables, connected by + or - • Variable - a quantity whose value can change, a letter• Constant • Coefficient - Factor the variable is multiplied by

Terminology

• Power • Exponent • Base

Representing Powers

• Term – part of an algebraic expression, separated by addition or subtraction

• Degree of a term – is the sum of the exponents on the variables

has degree 4

Representing Algebraic Expressions

You try:

Check your understanding pg. 80 #1,2

Practising pg. 81 #3,4,5, 6

*the opposite of square is square root = x

Multiplying and Dividing Powers• Powers in expanded form

• When multiplying Powers, add the exponents

Multiplication Expanded Form Product as single power

( (2) x (2) =

( (2) x (2 x 2) =

( (2 x 2) x (2 x 2) =

( (2 x 2) x (2 x 2 x 2) =

( (2 x 2) x (2 x 2 x 2 x 2) =

• Dividing Powers

• When dividing powers, subtract the exponents

Division Expanded form Quotient, as single Power

Representing expressions involving powers

• Simplify

= = = = = 4

Write as a single power

= (

= (

= (

=

Simplify when x = 2, y = 3.

= = = =xy= (2)(3)= 6

You try:

Check your understanding pg.89 #1,2,3,4

Practising pg. 90 #5-9 (bc), 10, 11-12 (bc)

Power of a Power• Is a Power raised to an exponent• 2

• when expanding a power of a power, multiply the exponents

Power of a power Expanded form Single power

( (

( ((

Simplify , when x is 3, y is 4.

= = = = = = (2)(= (2)(8)(4)= 64

You try:

Check your understanding pg. 96 #1,2

Practising pg.96-97 #3-12 (ab)