Chapter 3 Review.notebook 1 June 07, 2016 Final Exam Review Chapter 3 Polynomials and Factoring Multiplying Polynomials Distributive Property: used to multiply a single term (in front) and two or more terms inside a set of parentheses. 3x(2x + 4) 3x 2 y 3 (2xy 4 3x 2 y 2 5y)
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Chapter 3 Review.notebook
1
June 07, 2016
Final Exam Review
Chapter 3
Polynomials and Factoring
Multiplying Polynomials
Distributive Property: used to multiply a single term (in front) and two or more terms inside a set of parentheses.
3x(2x + 4) 3x2y3(2xy4 3x2y2 5y)
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FOIL:
(2x 3)(x + 4) (3x + 2)(2x2 x 3)
(2x 1)(x + 2) (4x 3)(x + 2)
Prime Factorization
Write the following as a product of prime factors:
2400
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Greatest Common Factor and Least Common Multiple
GCF: Find the COMMON factors. Multiply the LOWEST powers for each factor
LCM: Multiply the GREATEST power for EACH factor
Find the GCF and LCM of 40 and 72
40 72
Factoring Review
Remember, the first kind of factoring we look for is a Common Factor.
it is the largest number and/or variable that will divide into EACH of the terms in the expression.
Ex.
16x3 4x2 + 8x 16m4n5 8m3n2
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Second, look to see how many terms are in the expression.
If there are two terms, look to see if it a difference of squares:
two terms, both are perfect squares, one is positive and one is negative
Ex.
m2 9n2 50y2 + 8x2 m4 1
Third, if there are three terms try one of the following:
a) Decompostion
form ax2 + bx + c
look for two terms that multiply together to give you the product of ac and add to give you b.
keep the first and last term, and replace the middle term with these numbers (be sure to keep the variable with each number in the middle term).
group the first two terms together and the last two terms together, and take out a common factor from each group (**remember that you want the numbers in the brackets to be identical).
write out the factors.
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Ex.
a) 6x2 + 13x 5 b) 12x2 + 34xy 28y2
b) Short Trinomials
form ax2 + bx + c, where a = 1
look for two numbers that multiply to c, and add to give you b
Ex.
a) x2 5x 6 b) 2x3 2x2 24x
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c) Perfect Square Trinomials
first and last terms are perfect squares
remember, always check the middle term (should be double the square root of the first and last terms).
a2 + 2ab + b2 OR a2 2ab + b2
you will end up with identical factors.
ex.
a) 4x2 20x + 25 b) 9x2 24x 16
c) 16x4 8x2 + 1
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