University:
Glendale Community College
Course:
MAT120 | Intermediate Algebra
Academic year:

2020
Views:

69

Pages:

2
Author:

izbra0p

Section 1.7: A Review of all the Factoring Strategies – Mixed Up One of the hardest things about factoring is knowing which strategy to use. I will attempt to help you understand when to use a specific strategy as I go through this section with you. Here are a few tips that may help. 1) ALWAYS FACTOR OUT THE GCF FIRST IN EVERY FACTORING PROBLEM!!! If you don’t factor out the GCF it will likely be hard to determine which technique is needed to finish factoring. 2) Problems with 4 terms – FACTOR BY GROUPING. Here are a few examples of problems that I would factor by grouping. I will get more specific on how to factor these kinds of problems as I work through the section. x2 + 5x + 6x + 30 6y2 - 15y - 4y + 10 3) Problems with 3 terms – break these into two groups. The easier will contain the problems that do not have a number in front of the first term. The harder will have a number in front of the first term. (All problems with 3 terms can be factored using grouping, but I rarely use grouping to factor problems with three terms.) a) Problems with 3 terms that do not have a number in front of the first term. You can immediately create two parenthesis and put in the firsts and the signs. You will need to make a table to determine the lasts. Problems in original problem Signs in the factored answer + + ( + )( + ) - + ( - )( - ) + - ( + )( - ) - - ( + )( - ) A trick to remember this is if the second sign in the original problem is minus you get one parenthesis with a plus and one with a minus. If the second sign in a problem is plus you get the same sign in each parenthesis, and you refer back to the first sign. Here are a few examples of problems that fit this category. x2 + 5x – 6 y2 – 3y + 2 . Section 1.7: A Review of all the Factoring Strategies – Mixed Up b) Problems with 3 terms that have a number in front of the first term. Use BOTTOMS UP The steps for bottoms up Multiply Factor Divide / Reduce / Bottoms Up Here are a few examples of problems that fit this category. 3x2 + 4x – 7 5y2 – 14y + 8 4) Problems with 2 terms. First classify the problem as a square or a cube. a) Square problems have letters with exponents that are multiples of 2, such as x 2, y4, z6. They have numbers that are perfect squares such as 1, 4, 9, 16, 25, 49… i) Square problems with a plus sign are called sums of squares and are prime. Here are a few examples of problems that fit this category. 9x2 + 16 y2 + 49 ii) Square problems with a minus sign are called difference of squares and they factor. You divide the exponent of any letter by 2 and square root any number. Then create two essentially identical parenthesis. Here are a few examples of problems that fit this category. 9x2 - 16 y2 - 49 b) Cube problems have letters with exponents that are multiples of 3, such as x3, y6, z9. They have numbers that are perfect cubes such as 1, 8, 27, 64, 125. Cube problems with plus signs and minus signs both factor. The signs you put in the parenthesis are found by S.O.P. (same, opposite, plus). We then write what makes each piece a cube the put one of each in the first parenthesis and pair them up for the second parenthesis. Here are a few examples of problems that fit this category. x3 + 64 125y3 – 8 27x6 – 8x9