Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Factoring Trinomials Whose Leading Coefficient is NOT "1" - Section 6.3 We now want to factor polynomials of the form ax 2 bx c where a, b, and c are real numbers with a 0 or 1. We will consider two methods: Trial-and-Error and Grouping or ac-Method. Trial-and-Error Method: First factor out any GCF other than 1 from the polynomial. Assume that the polynomial is now in the form ax 2 bx c. 1. Find two first terms whose product is ax 2 x x ax 2 bx c 2. Find the last two terms whose product is c x x ax 2 bx c 3. By trial and error, continue to perform steps 1 and 2 until the sum of the inner and outer products is bx x x ax 2 bx c If no such combination exists, then the polynomial is prime. Examples: Factor 1. 5x 2 14x 8 1 2. 6x 2 19x 7 Some helpful hints and suggestions for factoring ax 2 bx c using trial-and-error: 1. If b is relatively small, avoid the larger factors of a. 2. If c is positive, the signs in both binomial factors must match the sign of b. 3. If the trinomial has no common factor, than no binomial factor can have a common factor. 4. Reversing the signs in the binomial factors changes the sign of the middle term bx. Factor 6x 2 x 12 using trial-and error. Use some of the helpful hints and suggestions from above. 2 Factoring by the Grouping Method (or ac -Method): To factor ax 2 bx c 1. Calculate the product ac. 2. Find to factors, m and n, such that mn ac and m 3. Rewrite the trinomial as ax 2 c and factor by grouping. mx nx n b. Examples: Factor 1. 3x 2 x 2. 8a 2 3a 10 5 3 3. 12x 2 4. 3x 2 23x 5x 10 4 Factoring Trinomials in Two Variables: 5. Factor 3x 2 13xy 4y 2 by trial-and-error 4 6. Factor 3x 2 31xy 22y 2 by the grouping method Factor the following polynomials COMPLETELY. Remember to start with factoring out the GCF. 7. 5y 4 13y 3 6y 2 5 8. 4x 3 9. 12a 2 b 2x 2 90x 21ab 2 6b 3 6