day 138 and 139 april 18 and 19 combine like terms days 1...
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day 138 and 139 april 18 and 19 Combine Like Terms days 1 and 2 polynomials.notebook
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April 18, 2016
www.njctl.org
Algebra I
Polynomials
www.njctl.org
20130731
Table of Contents
Table of Contents
• Definitions of Monomials, Polynomials and Degrees• Adding and Subtracting Polynomials
• Multiplying Polynomials• Mulitplying a Polynomial by a Monomial
• Special Binomial Products• Solving Equations • Factors and GCF• Factoring out GCF's
• Factoring 4 Term Polynomials
• Identifying & Factoring x2+ bx + c
• Factoring Using Special Patterns• Factoring Trinomials ax2 + bx + c
• Mixed Factoring• Solving Equations by Factoring
day 138 and 139 april 18 and 19 Combine Like Terms days 1 and 2 polynomials.notebook
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Add/Subt Poly
Adding and Subtracting Polynomials
Essential understanding: You
Warm Up:
What do you need in order to combine like terms? Explain your answer and give an example of like terms.
Today, we will begin our polynomials unit.
Apr 811:11 AM
Warm up: Day 2 of Combining like terms
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Warmup:
Today, we will continue adding & subtractingpolynomials. Please have yesterday's homework out.
Add/Subt Poly
Standard Form
The standard form of an equation is to put the terms in order from highest degree to the lowest degree.
Standard form is commonly excepted way to write polynomials.
Example: is in standard form.
Put the following equation into standard form:
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Monomials with the same variables and the same power are like terms.
Like TermsUnlike Terms 4x and 12x 3b and 3a x3y and 4x3y 6a2b and 2ab2
Add/Subt Poly
Combine these like terms using the indicated operation.
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1 Simplify
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Pull
Pull
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2 Simplify
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B C D
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Pull
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3 Simplify
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B
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Pull
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To add polynomials, combine the like terms from each polynomial.
To add vertically, first line up the like terms and then add. Examples:(3x2 +5x 12) + (5x2 7x +3) (3x4 5x) + (7x4 +5x2 14x)
line up the like terms line up the like terms 3x2 + 5x 12 3x4 5x (+)5x2 7x + 3 (+) 7x4 +5x2 14x 8x2 2x 9 10x4 +5x2 19x
=
day 138 and 139 april 18 and 19 Combine Like Terms days 1 and 2 polynomials.notebook
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We can also add polynomials horizontally. (3x2 + 12x 5) + (5x2 7x 9)
Use the communitive and associative properties to group like terms.
(3x2 + 5x2) + (12x + 7x) + (5 + 9)
8x2 + 5x 14
Add/Subt Poly
4 Add
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B C D
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Pull
day 138 and 139 april 18 and 19 Combine Like Terms days 1 and 2 polynomials.notebook
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5 Add
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6 Add
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B C D
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7 Add
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8 Add
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B C D
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To subtract polynomials, subtract the coefficients of like terms.
Example: 3x 4x = 7x
13y (9y) = 22y
6xy 13xy = 7xy
Add/Subt Poly
We can subtract polynomials vertically and horizontally.
To subtract a polynomial, change the subtraction to adding 1. Distribute the 1 and then follow the rules
for adding polynomials(3x2 +4x 5) (5x2 6x +3)
(3x2+4x5) +(1) (5x26x+3)(3x2+4x5) + (5x2+6x3)
3x2 + 4x 5 (+) 5x2 6x + 3
2x2 +10x 8
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We can subtract polynomials vertically and horizontally.
To subtract a polynomial, change the subtraction to adding 1. Distribute the 1 and then follow the rules
for adding polynomials(4x3 3x 5) (2x3 +4x2 7)
(4x3 3x 5) +(1)(2x3 +4x2 7)(4x3 3x 5) + (2x3 4x2 +7)
4x3 3x 5 (+) 2x3 4x2 + 7 2x3 4x2 3x + 2
Add/Subt Poly
We can also subtract polynomials horizontally.(3x2 + 12x 5) (5x2 7x 9)
Change the subtraction to adding a negative one and distribute the negative one.(3x2 + 12x 5) +(1)(5x2 7x 9)(3x2 + 12x 5) + (5x2 + 7x + 9)
Use the communitive and associative properties to group like terms.(3x2 +5x2) + (12x +7x) + (5 +9)
2x2 + 19x + 4
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9 Subtract
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10 Subtract
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11 Subtract
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12 Subtract
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B C D
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13 Subtract
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14 What is the perimeter of the following figure? (answers are in units)
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Day 1 Homework: Complete the Simplifying Variable Expressions worksheet and Exponent Rules worksheet
Apr 811:17 AM
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April 19 Day 2 In Class Work: Complete the Simplifying Variable Expressions
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April 19 Day 2 Classwork: 5-1 worksheet
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day 138 and 139 april 18 and 19 Combine Like Terms days 1 and 2 polynomials.notebook
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Polynomials
Day 2 April 19 Homework: Complete the Adding and Subtracting Polynomials worksheet
Apr 1412:42 PM
day 138 and 139 april 18 and 19 Combine Like Terms days 1 and 2 polynomials.notebook
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Apr 1412:42 PM
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