Polynomials & Properties of Exponents AKS: 1, 2 & 3

Vocabulary  The terms are the parts of an expression that are added together.  The coefficient of the term is the number part of a term with a variable.  A constant term has a number part but no variable part.  Like terms are terms that have the same variable parts.  EX 1: Identify the terms, coefficients, constants: -x + 2x + 8

Vocabulary  The degree of a polynomial is the highest exponent.  1,2 and 3  Standard form is when a polynomial is written so that the exponents decrease from left to right.  The coefficient of the first term in Standard Form is called the leading coefficient.  EX 2: Put the following polynomials in order so the exponents decrease from left to right and name the leading coefficient and degree of the polynomial. a) 5x³ x b) x – 4x³ + x² c) -5 + x 8 – x 5

Adding Polynomials  When adding polynomials, like terms are combined. ***Exponents do not change when adding***  EX 3: (3x 4 – 2x 3 + 5x²) + (7x² + 9x 3 – 2x)

Practice 1. (8x² - 2x + 7) + (9x² + 6x – 11) 2. (4x – 3 – 5x³) + (3x² - 8x + 2)

Subtracting polynomials  When subtracting polynomials, distribute the negative to all terms in the second polynomial and then combine like terms.  EX 4: (2x³ - 5x² - 5) – (4x³ - 5x² + x – 4)

Practice 3. (3x² - 8x + 3) – (9x + 2x² - 8) 4. (5x x² + 3x³) – (8x³ - 3x² + 5)

Multiplication / Product of Powers

YOU TRY: Multiply

Power of a Power

You Try: Power of a Power

Division / Quotient of Powers

You Try: Quotient of Powers

Power of a Quotient

You Try: Power of a Quotient

Power of a Product

You Try: Power of a Product

Negative & Zero Exponents

You Try: Negative & Zero Exponents

Extra Practice / TOTD Evaluate the expression

Extra Practice / TOTD Simplify the expression

Distributive Property  The Distributive Property is an algebraic property which is used to multiply a single term and two or more terms inside a set of parentheses.  Example: 3(x + 6) = 3(x) +3(6) How would I simplify this expression after I distributed?

Practice 1. What is wrong here? 4(y + 3) = 4y (y + 7)y n(n – 9) 4. (2 – n)(2/3)

More Practice 5. -2(x + 7)6. (5 – y)(-3y) 7. – (2x – 11)8. (1/2)(2n + 6)

Try this!  Simplify the expression: 4(n+9) – 3(2 +n)  What did you do first and why?

Practice Simplify the expression: 9. (4a – 1)2 + a10. -6(v + 1) + v 11. 7(w – 5) + 3w12. (s – 3)(-2) +17s

Geometry  Find the perimeter and area of the rectangle: v + 3 5

You Try! – 12w X Find the perimeter and area of the rectangle.

Challenge! Translate the verbal phrase into an expression then simplify. 1. Twice the sum of 6 and x, increased by 5 less than x. 2. Three times the difference of x and 2, decreased by the sum of x and 10.