The Math World
Factoring
Always look for a Greatest Common Factor FIRST!!!
2 TERMS 3 TERMS 4 TERMS
(Must be in one of the following forms (X or Pattern) (Grouping)
to factor with two terms)
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OR
Difference of Cubes - SOAP
a3 - b3 = (a-b)(a2 + ab + b2)
Guess and check
1. List the factors for the first coefficient and the constant.
2x2 + 3x - 5
2 = 2, 1 5 = 5, 1
2. Place the 1 set of factor in the parenthesis. FOIL to check.
(2x + 1)(x – 5) or (2x – 5)(x + 1)
2x2 – 9x – 5 2x2 – 3x – 5
3. If you numbers are correct except for the signs, simply change the signs.
(2x + 5)(x – 1)
2x2 + 3x – 5
1. If nothing can be done to the original expression, then it is PRIME 2. Check to see if any of your final answers will factor further. 3. Check your answer by multiplying.
Write the binomial times the binomial created by the terms left when GCF. binomial was pulled out.
(x – 4 )(2x2 + 3)
Group first two and last two terms and see if each pair has a G.C.F. (May need to change order of the terms)
2x3 – 8x2 + 3x - 12
If the G.C.F. of each pair results in a common binomial, factor out the binomial..
2x2(x – 4) + 3(x – 4)
THEN
THEN
Sum Of Cubes - SOAP
a3 + b3 = (a+b)(a2-ab + b2)
OR
Difference of Two Perfect Squares
a2 – b2 = (a + b)( a - b)
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