EXTENDED ALGEBRA EXTENDED ALGEBRA TOPICS DAY 1TOPICS DAY 1

MATH 7MATH 7

CHAPTER OVERVIEWCHAPTER OVERVIEW In this chapter we will build on the algebra In this chapter we will build on the algebra

topics that we have already learned.topics that we have already learned. Topics we have already discussed:Topics we have already discussed:

Translating Verbal Expressions to Algebra Translating Verbal Expressions to Algebra ExpressionsExpressions

Solving One and Two Step Equations (with Solving One and Two Step Equations (with and without negatives)and without negatives)

Terms of an ExpressionTerms of an Expression

The The termsterms of an algebraic expression are the of an algebraic expression are the individual pieces of that expressionindividual pieces of that expression Example: 3x + 2Example: 3x + 2

3x and 2 are both individual terms of the expression3x and 2 are both individual terms of the expression

How many terms does this expression have?How many terms does this expression have?

POLYNOMIALSPOLYNOMIALS

A A polynomialpolynomial is an algebraic expression is an algebraic expression that contains one or more terms.that contains one or more terms. Example: 7x + 9, 5x – 12, 3xExample: 7x + 9, 5x – 12, 3x22 – 2x + 9, – 2x + 9,

12x, 15x,12x, 15x, 13x – 11 13x – 11

These are all polynomials.These are all polynomials.

SPECIFIC TYPES OF SPECIFIC TYPES OF POLYNOMIALSPOLYNOMIALS

MonomialMonomial – a polynomial that has only – a polynomial that has only one termone term ex. 4x, -9x, etc.ex. 4x, -9x, etc.

BinomialBinomial – a polynomial that has exactly – a polynomial that has exactly two termstwo terms ex. 3x – 9 , -5x + 6 etc.ex. 3x – 9 , -5x + 6 etc.

TrinomialTrinomial – a polynomial that has – a polynomial that has exactly three termsexactly three terms ex. 2xex. 2x22 + 6x + 3 + 6x + 3

ADDING AND SUBTRACTING ADDING AND SUBTRACTING MONOMIALSMONOMIALS

Two or more monomials of the same Two or more monomials of the same variable can be combined into one variable can be combined into one monomial by addition or subtraction.monomial by addition or subtraction.

Follow the same rules for normal addition Follow the same rules for normal addition or subtraction (watch out for negatives)or subtraction (watch out for negatives) Ex. 3x + 12x = 15xEx. 3x + 12x = 15x

MORE EXAMPLESMORE EXAMPLES

7x – 3x ___7x – 3x ___ 12x + 11x ___12x + 11x ___ 9x + (-2x) ___9x + (-2x) ___ -11x – 5x ___-11x – 5x ___ 9x – 13x ___9x – 13x ___ 5x + 7x – 4x ___5x + 7x – 4x ___ -6x + 4x – 8x ___-6x + 4x – 8x ___

HOMEWORKHOMEWORK

Complete the Worksheet (Extended Complete the Worksheet (Extended Algebra – Polynomials)Algebra – Polynomials)