Name________________
Unit 5 Name______________________________
Polynomials
|Day 1 |Adding & Subtracting Polynomials |
|Day 2 |Multiplying & Dividing Monomials and Power Rules |
|Day 3 |QUIZ |
|Day 4 |Multiply Polynomials |
|Day 5 |Multiply Polynomials |
|Day 13 |Unit 5 Review |
|Day 14 |Unit 5 TEST |
Unit 5 Vocabulary:
|Word |Meaning |Where to find more info |
|Base | | |
|Binomial | | |
|Coefficient | | |
|Degree | | |
|Exponent | | |
|Monomial | | |
|Polynomial | | |
|Standard Form | | |
|Trinomial | | |
|Variable | | |
|Operation |Rule |Where to find more info |
|Add | | |
|Divide |_____________ coefficients, _____________ exponents | |
|Multiply |_____________ coefficients, _____________ exponents | |
|Negative Exponents | | |
|Power to Power |_____________ coefficients, _____________ exponents | |
|Subtract | | |
|Subtracted From | | |
[pic]
|# of terms |name |example |
|1 term |monomial |3x2 |
|2 terms |binomial |3x2 + x |
|3 terms |trinomial |3x2 + x + 1 |
|many terms |polynomial |x3 + 2x2 – x + 5 |
¤The degree of a polynomial is the________________________________________.
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|1) x3 + 4x2 + 1 degree________ |2) x2 + x + 1 degree________ |
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|3) x – 3 degree________ |4) 6 degree________ |
¤Standard Form
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|Arrangement of variables from ________________________ to _______________________, |
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|From __________________________ to __________________________ degree of power. |
|5) 8 + 3p2 + 4p |6) x – 4 + 11x3 + 16x4 – 2x2 |
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¤Adding Polynomials:
Leave all signs the way they are and combine LIKE TERMS, don’t touch exponents.
Remember: Like terms have the EXACT SAME variable, EXACT SAME exponent!
|7) [pic] |8) [pic] |
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¤Subtracting Polynomials:
Distribute a –1 through the second set of parentheses, then combine like terms.
|9) [pic] |10) [pic] |
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¤Subtracted From: When the problem says SUBTRACTED FROM, remember that
what follows the from always goes first!
|11) If 5x2 – 8 is subtracted from 12x² + 5, find the result. |12) Subtract x² + 2x from –x² + x. |
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¤One step further:
|13) [pic] |14) [pic] |
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[pic]
[pic]
[pic]
_______________
3x2
_________________ ________
[pic]
[pic] Rule: When multiplying like bases, _______________ coefficients, _______________ exponents!
Examples:
|1) [pic] |2) [pic] |3) [pic] |
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|4) [pic] |5) [pic] |6) [pic] |
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[pic]
[pic] Rule: When dividing like bases, _______________ coefficients, _______________ exponents!
Examples:
|7) [pic] |8) [pic] |9) [pic] |
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|10) [pic] |11) [pic] |
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[pic]
[pic]
[pic]
So: [pic]
Examples:
|12) [pic] |13) [pic] |14) [pic] |
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[pic]
[pic]
[pic]
|[pic] RULE: [pic] |
|[pic] __________ coefficient to __________, _______________ exponents |
Examples:
|1) [pic] |2) [pic] |3) [pic] |
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Multiplying Polynomials
|¤In order to multiply 2 binomials, we have to double distribute. |
|You distribute the first term, then you distribute the second term. |
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|Multiply: [pic] = _____ + _____ + _____ + _____ |
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|Then make sure to combine any like terms. Final answer: _______________ |
|¤Another method you could use is the box method: |
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|Again, make sure to combine any like terms. |
|Final answer: _______________ |
|(It should be the same answer as above!) |
Let’s Try It:
|4) [pic] |5) [pic] |6) [pic] |
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[pic]
|7) [pic] |8) [pic] |
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[pic] Multiply the polynomials below, you may use whichever method you find easier.
|9) [pic] |10) [pic] |
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|11) [pic] |12) [pic] |
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[pic]
Cubing a binomial:
|1) [pic] |2) [pic] |
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|3) [pic] |4) [pic] |
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|Remember that multiplying polynomials is just |
|doing the Distributive Property multiple times! |
5) Use the distribution method to solve this problem: [pic]
6) Multiply using the Grid Method: [pic]
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Practice:
Multiply the following polynomials using either the Distribution Method or the Grid Method.
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7) [pic]
8) [pic]
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-----------------------
x 1 = _____
x 0 = _____
[pic]
Distribute the x
Distribute the 3
| |x |+3 |
|x | | |
|+2 | | |
Steps:
1. Put polynomials on outside of box
2. Multiply corresponding parts
3. Pull out all pieces from the box
4. Combine like terms
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