Question

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 1

I need ideas not answers.

Answer 2

Well there are two ways I can think of.
There are two strategies for factoring expressions of this kind that I know of.
If I were to give you 2x^2-x-3, how would you attempt to factor this?

Answer 3

I do not know. :( I was thinking of something along the lines like 2x^2+13x+15.

Answer 4

Ok let me ask you another question.
Do you know how to multiply this: (2x-3)(x+1)?

Answer 5

FOIL

Answer 6

Ok. What do you get as the product?

Answer 7

Show the steps if you don't mind.

Answer 8

(1 + x)(3 + 2x)

Multiply (1 + x) * (3 + 2x)
(1(3 + 2x) + x(3 + 2x))
((3 * 1 + 2x * 1) + x(3 + 2x))
((3 + 2x) + x(3 + 2x))
(3 + 2x + (3 * x + 2x * x))
(3 + 2x + (3x + 2x2))

Combine like terms: 2x + 3x = 5x
(3 + 5x + 2x2)

Answer 9

Ok well you wrote a different problem, but that is fine. We can use this one too...
So we have (1+x)(3+2x)=3+2x+3x+2x^2
(x+1)(2x+3)=2x^2+3x+2x+3

Now if we look at these:
Problem 1:
(x-2)(2x+9)=2x^2+9x-4x-18

Problem 2:
(2x+3)(3x-1)=6x^2-2x+9x-3


Problem 3:
(5x-2)(3x+1)=15x^2+5x-6x-2


Do you see any patterns going on here or relationships you notice?