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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.