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
Objective The student will be able to: factor trinomials with grouping. Factoring Chart This chart will help you to determine which method of factoring to use. Type Number of Terms 1. GCF 2 or more 2. Diff. Of Squares 2 3. Trinomials 3 Review: (y + 2)(y + 4) y2 +4y +2y +8 First terms: Outer terms: Inner terms: Last terms: Combine like terms. y2 + 6y + 8 y +2 y2 +2y +4 +4y +8 y In this lesson, we will begin with y2 + 6y + 8 as our problem and finish with (y + 2)(y + 4) as our answer. Here we go! 1) Factor y2 + 6y + 8 Use your factoring chart. Do we have a GCF? No Is it a Diff. of Squares problem? No 3 terms Now we will learn Trinomials! You will set up a table with the following information. Product of the first and last coefficients Middle coefficient The goal is to find two factors in the first column that add up to the middle term in the second column. We’ll work it out in the next few slides. 1) Factor 2 y M A + 6y + 8 Create your MAMA table. Product of the first and last coefficients Multiply +8 Add +6 Middle coefficient Here’s your task… What numbers multiply to +8 and add to +6? If you cannot figure it out right away, write the combinations. 1) Factor 2 y + 6y + 8 Place the factors in the table. Multiply +8 Which has a sum of +6? +1, +8 -1, -8 +2, +4 -2, -4 Add +6 +9, NO -9, NO +6, YES!! -6, NO We are going to use these numbers in the next step! 1) Factor y2 + 6y + 8 Multiply +8 Add +6 +2, +4 +6, YES!! Hang with me now! Replace the middle number of the trinomial with our working numbers from the MAMA table y2 + 6y + 8 y2 + 2y + 4y + 8 Now, group the first two terms and the last two terms. We have two groups! (y2 + 2y)(+4y + 8) Find the GCF of each group and factor it out. If things are done y(y + 2) +4(y + 2) Factor out the GCF’s. Write them in their own group. right, the parentheses should be the same. (y + 4)(y + 2) There’s your answer…(y + 4)(y + 2) You can check it by multiplying. M A 2) Factor x2 – 2x – 63 Create your MAMA table. Product of the first and last coefficients Signs need to be different since number is negative. Multiply -63 -63, 1 -1, 63 -21, 3 -3, 21 -9, 7 -7, 9 Add -2 -62 62 -18 18 -2 2 Middle coefficient Replace the middle term with our working numbers. x2 – 2x – 63 x2 – 9x + 7x – 63 Group the terms. (x2 – 9x) (+ 7x – 63) Factor out the GCF x(x – 9) +7(x – 9) The parentheses are the same (x + 7)(x – 9) Here are some hints to help you choose your factors in the MAMA table. 1) When the last term is positive, the factors will have the same sign as the middle term. 2) When the last term is negative, the factors will have different signs. M A 2) Factor 5x2 - 17x + 14 Create your MAMA table. Product of the first and last coefficients Signs need to be the same as the middle sign since the product is positive. Multiply +70 -1, -70 -2, -35 -7, -10 Add -17 -71 -37 -17 Replace the middle term. 5x2 – 7x – 10x + 14 Group the terms. Middle coefficient (5x2 – 7x) (– 10x + 14) Factor out the GCF x(5x – 7) -2(5x – 7) The parentheses are the same (x – 2)(5x – 7) Hopefully, these will continue to get easier the more you do them. Factor 1. 2. 3. 4. (x + 2)(x + 1) (x – 2)(x + 1) (x + 2)(x – 1) (x – 2)(x – 1) 2 x + 3x + 2 Factor 1. 2. 3. 4. (2x + 10)(x + 1) (2x + 5)(x + 2) (2x + 2)(x + 5) (2x + 1)(x + 10) 2 2x + 9x + 10 Factor 1. 2. 3. 4. 2 6y (6y2 – 15y)(+2y – 5) (2y – 1)(3y – 5) (2y + 1)(3y – 5) (2y – 5)(3y + 1) – 13y – 5 2) Factor 2x2 - 14x + 12 Find the GCF! 2(x2 – 7x + 6) Now do the MAMA table! Signs need to be the same as the middle sign since the product is positive. Multiply +6 Add -7 -1, -6 -7 -2, -3 -5 Replace the middle term. 2[x2 – x – 6x + 6] Group the terms. 2[(x2 – x)(– 6x + 6)] Factor out the GCF 2[x(x – 1) -6(x – 1)] The parentheses are the same 2(x – 6)(x – 1) Don’t forget to follow your factoring chart when doing these problems. Always look for a GCF first!!