Mayansky/Finizio .k12.nj.us
Mayansky/Finizio
Period 5/6
Algeo I
Quiz Date: 4/21/05
Sections 5.3-5.5
Study Guide
(KEY)
Sample Problem #1
Divide
[pic]
[pic]
[pic]
Sample Problem #2
Find the greatest monomial factor. Then factor the given polynomial
[pic]
The greatest common factor between these two is:
[pic]
[pic]
[pic]
[pic]
Sample Problem #3: Method 1
Simplify
[pic]
[pic]
[pic]
[pic]
Sample Problem #4: Method 2 (F.O.I.L.) First Outer Inner Last
Simplify
[pic]
[pic] [pic] [pic] [pic]
[pic]
[pic]
Sample Problem #5
Write the product as a binomial
[pic]
[pic]
[pic]
Sample Problem #6
Factor
[pic]
[pic]In order to write this you must know the following formula.
[pic]
[pic]
[pic]
Therefore from our formula above z = a and 7 = b.
[pic]
Practice Problems
|Divide |Divide |Divide |Divide |
|[pic][pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
|Divide |Divide |Divide |Divide |
|[pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
|Factor |Factor |Factor |Factor |
|[pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
|Factor |Solve |Solve |Solve |
|[pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
|Solve |Solve |Solve |Solve |
|[pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
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|Write as a Binomial |Write as a Binomial |Write as a Binomial |Write as a Binomial |
|[pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
|Write as a Binomial |Write as a Binomial |Write as a Binomial |Write as a Binomial |
|[pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
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|Factor |Factor |Factor |Factor |
|[pic] |[pic] |[pic] |[pic] |
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|[pic] |[pic] |[pic] |[pic] |
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Step#1: Multiply the two first terms of the parenthesis, multiply the outer terms in parenthesis, multiply the inner terms of parenthesis, and multiply the last terms in parenthesis.
Step#2: Multiply
Last Terms
Inner Terms
Outer Terms
First Terms
Step #3:.Add or subtract like terms. In this case 20s and -20s are like terms.
Simplified
Step #1: Divide 6a by 3 and 9 by 3.
Step #2: Simplify (Final Answer)
Step #1: Find the greatest common factor between [pic] and[pic].
Step #2: Place 4y on the outside of the parenthesis and divide [pic]and [pic] by 4y to get the terms inside the parenthesis.
Step #3: Simplify
Final Answer
Step #1: Multiply the 1st term (4s) in the first set of parenthesis by the polynomial in the second parenthesis (4s+5). Also multiply the 2nd term (-5) in the first parenthesis by the polynomial in the second parenthesis (4s+5).
Step #2: Distribute all numbers outside the parenthesis. By doing this you will remove your parenthesis.
Step #3:.Add or subtract like terms. In this case 20s and -20s are like terms.
Simplified
Step #1:.Recogonize the pattern in this problem. In the first parenthesis you have x+3 and in the second parenthesis you have x-3. If you see a pattern like this there is a short cut to solving this problem. .
Step #2: Square the first term in the first parenthesis (X) and the second term in the first parenthesis (+3)
Place a subtraction sign in between these two.
Step #3: Simplify.
Final Answer
Step #1:.Recogonize that this is the difference between 2 perfect squares.
Step #2:.find the square root of [pic]and [pic].
Step #3:.Plug the numbers into your formula.
Final Answer
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