# Lesson 90 – Doodles Do Algebra

These in the next few lessons, we finish off the ideas of factoring and begin to look at the greatest common factor.

Today your child learns how to separate a quadratic trinomial into its factors. DoodleOne explains it very nicely, so I will let her do it on the worksheet.

If your child has trouble, just work through a few with her and show her that the process is kind of like working out ciphers using a couple of clues. You are given two numbers, one that represents a times b, and the other that represents either a plus b or a minus b or b minus a. Then you have to work out values for a and b are and that tells you what the factors of the quadratic trinomial. It all sounds much more complicated than it really is.

1. $(x+2)(x+3)$ The idea here is to think of possible factors for 6 (like 2*3 or 6*1) and then decide if either of those possiblilities can be combined to make 5. Since 2+3 is 5, then you get your factors for the equation.

2. $(a+3)(a+4)$ So here you think of ways to factor 12 (like 12*1, 2*6, or 3*4) and then figure out which set combines to make 7. 3+4 is 7, so the values for a and b are 3 and 4.

3. $(x-2)(x-3)$ Here you have to find factors for 6, keeping in mind that they mst combine to a negative 5. Following the same process as the last 2 problems, you decide that -2*-3 are the best factors because they add to -5 and multiply to yield a +6.

4. $(x-10)(x+1)$

5. $(x+3)(x-2)$

6. $(x+2)(x-1)$

7. $(x-8)(x-5)$

8. $(x-8)(x+1)$

9. $(x-9)(x+2)$

10. $(x-6)(x+5)$

11. $(3)(x^2+4x-5)=3(x-5)(x+1)$