After studying this lesson, you will be able to: - Factor various types of problems.
**Steps of Factoring: **
1. Factor out the GCF 2. Look at the number of terms: - 2 Terms: Look for the Difference of 2 Squares
- 3 Terms: Factor the Trinomial
- 4 Terms: Factor by Grouping
3. Factor Completely 4. Check by Multiplying This section is a review of the types of factoring we'vecovered so far. Follow the steps listed above to factor theproblems. **Example 1**
Factor 3x^{ 2} - 27 1^{ st }: Look for a GCF....the GCF is 3 so we factorout 3: 3( x^{ 2} - 9) 2^{ nd} : Look at the number of terms in theparenthesis. There are 2 terms and it is the difference of 2squares. We factor the difference of 2 squares (keeping the 3).3(x + 3) ( x - 3) 3^{ rd} : Now, make sure the problem is factoredcompletely. It is. 4^{ th }: Check by multiplying. **Example 2 **
Factor 9y ^{2} - 42y + 49 1^{ st} : Look for a GCF....the GCF is 1 so we don'thave to worry about that. 2^{ nd} : Look at the number of terms. There are 3terms so we factor the trinomial. -make 2 parentheses -using the sign rules, we know the signs will be the samebecause the constant term is positive - we also know they will be negative because theinside/outside combination must equal -58y -find the factors of the 1 st term: 1y, 9y and 3y, 3y . Let'stry 3y, 3y -find the factors of the constant term: 1, 49 and 7, 7. Let'stry 7, 7 (3y - 7) (3y - 7) -check the inside/outside combination: inside we have -21y andoutside we have -21y which adds up to -42y 3^{ rd} : Now, make sure the problem is factoredcompletely. It is. 4^{ th} : Check by multiplying. **Example 3 **
Factor x^{ 3} - 5x^{ 2} - 9x + 45 1^{ st }: Look for a GCF....the GCF is 1 so we don'thave to worry about that. 2^{ nd }: Look at the number of terms. There are 4terms so we factor by grouping. Group the terms (x^{ 3} - 5x^{ 2} ) + (- 9x +45 ) Take the GCF of the each group: x^{ 2} (x^{ }-5 )(- 9(x - 5 )) Take the GCF of the entire problem: (x^{ }- 5 )(x^{2} -9) 3^{ rd }: Now, make sure the problem is factoredcompletely. It isn't. We can factor the second parenthesis. (x^{ }- 5 )(x + 3)(x - 3) 4^{ th} : Check by multiplying. |