Question

Near the beginning of Lesson 5.3, a strategy for factoring trinomials of the form x^2+ bx+c was

developed by exploring the product of the binomials (x+p) and (x+q).
Explain how the development of this factoring strategy is an example of working backwards
to solve a problem.

Answer 1

Explanation:

there are function that "invert" each other..

subtraction inverts addition...

3+2 = 5 ... 5-2 = 3

division inverts multiplication

5*2 = 10 ... 10/2 = 5

Using that concept, "factoring" is basically the inverse of multiplication

3x^2 + 9x can be factored to 3x(x+3)

if you multiply that out it reverts back to the original equation

so x^2 + 5x + 6 factors to (x+3)(x+2)

if you multiply that out (foil it)

you get x^2 + 5x + 6