Polynomials& Properties of ExponentsAKS: 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 - 4 + 3xb) x – 4x³ + x² c) -5 + x8 – x5

Adding Polynomials When adding polynomials, like terms are

combined. ***Exponents do not change when adding***

EX 3: (3x4 – 2x3 + 5x²) + (7x² + 9x3 – 2x)

Practice1. (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)

Practice3. (3x² - 8x + 3) – (9x + 2x² - 8)

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

Multiplication / Product of Powers

When you are multiplying like bases, then add the exponents.

YOU TRY: Multiply

Power of a Power When you are raising a power to

another power, then you multiply the exponents.

You Try: Power of a Power

Division / Quotient of Powers When you are dividing like bases,

subtract the exponents.

You Try: Quotient of Powers

Power of a Quotient When you are raising a quotient

(fraction) to a power, you must raise EACH part of the numerator and denominator to that power by multiplying the exponents.

You Try: Power of a Quotient

Power of a Product To find the power of a product, you must

raise each factor to the power by multiplying exponents.

You Try: Power of a Product

Negative & Zero Exponents

You Try: Negative & Zero Exponents

Extra Practice / TOTDEvaluate the expression.1. 2. 3. 4.

27 7 225

7

3

4

4

321

3

Extra Practice / TOTDSimplify the expression.1. 2. 3. 4.8

4

x

x 62 33 x 50 24 w 4 2 3 5y z y z

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?

Practice1. What is wrong here? 4(y + 3) = 4y + 3

2. (y + 7)y

3. 0.5n(n – 9)

4. (2 – n)(2/3)

More Practice5. -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?

PracticeSimplify the expression:9. (4a – 1)2 + a 10. -6(v + 1) + v

11. 7(w – 5) + 3w 12. (s – 3)(-2) +17s

Geometry Find the perimeter and area of the rectangle:

v + 3

5

You Try!

1. 2.

8 – 12w

9

2.1

X + 0.6

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.