Question

You are familiar with the following types of factoring:

factoring out the Greatest Common Factor (GCF)
factoring by grouping
factoring trinomials of the form x2 + bx + c and ax2 + bx + c
As you know, you need to know the first two types of factoring listed above in order to be successful in factoring trinomials of the form ax2 + bx + c.

Part 1:
In your own words, explain how a trinomial of the form 2x2 + 13x + 15 can be turned into a four term polynomial suitable for factoring by grouping. Use complete sentences.

Part 2:
If you were an Algebra 1 instructor and were creating a t

Answer 1

Part 2:
If you were an Algebra 1 instructor and were creating a test on factoring trinomials of the form ax2 + bx + c, what do you think would be the easiest way to create a trinomial that can be factored? Provide one unique example.

Answer 2

Part I
You do it the same way you would with any other trinomial. Find two numbers that multiply to get ac, but add to get b. In this case, it would be 10 and 3. Then you would use those numbers to "split the middle term" such that 13x = 10x + 3x and write the following steps

2x^2 + 13x+15
=2x^2 + 10x + 3x + 15
= 2x(x+5) + 3(x+5)
=(x+5)(2x+3)

Answer 3

ok

Answer 4

Part II

1. Select any two random numbers say 12 and 13.
2. Let a = 12 and c = 13.
3. Add them together to get 25
4. Let b = 25
5. Now you have a factorable trinomial:
12x^2 + 25x + 13

Answer 5

That's the "easiest" way. You can also use multiples of 25 to make it more interesting.

Answer 6

So 12x^2 + 50x + 13 would also work

Answer 7

oh ok

Answer 8

If you want to intentionally make one that isn't factorable, just make it

12x^2 + 49x + 13

Answer 9

oohhhh

Answer 10

Easy as pie, isn't it?

Answer 11

yeah it is, thank you