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Saturday, October 20, 2007
Section 13.1 (Introduction to Factoring)
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The greatest common factor (GCF) among 2 or more numbers is the largest number that is a
factor of all the numbers
Example: Find the GCF of 120, 180, and 420
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The GCF of monomials is the product of
o The GCF of the coefficients
o The variable(s) common in the monomials (use smallest exponent present for that variable)
Examples:
Find the GCF of 15x3, 30x2, and 40x5
Find the GCF of 16p3y, -10py, 40p2y2 and 12p
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Factoring a polynomial is essentially the reverse of multiplying monomials / polynomials
To factor a given polynomial, find the GCF of all terms, and write the answer as a product of the
GCF and the remaining terms (5x2 + 15 = (5)x2 + (5)3 = 5(x2 + 3))
Examples: Factor (check results)
7x3 + 21x2
2 3 1 2 4
x - x +
3
3
3
15x4 – 9x3 – 21x
16p6q4 + 32p5q3 – 48pq2
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Certain polynomials can also be factored by a method of grouping
Examples: Factor (by grouping)
x7(x + 5) + 8(x + 5) = x7A + 8A = (x7 + 8)A = (x7 + 8)(x + 5)
3x5(2x - 7) – (2x – 7) =
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A good place to start with a 4-term polynomial is by grouping the first 2 terms together,
factoring, and then factoring the last 2 terms
x3 + 6x2 + 4x + 24 = (x3 + 6x2) + 4x + 24 = x2(x + 6) + 4x + 24 = x2(x + 6) + 4(x + 6) = (x2 + 4)(x + 6)
20x3 – 12x2 + 35x – 21
5x3 – 5x2 – x + 1
20p3 – 4p2 -25p + 5
Additional Homework from Book: 4, 6, 11, 13, 17, 25, 29, 35, 37, 39, 43, 47, 51