Factoring trinomials in the form x^2 + bx + c.

Question

Explain why px + qx = (p + q)x. 

I understand how to apply this when factoring, but i don't really understand why the x is not added when the p and q aren't added.

 

Explain why the expression x2 + (p + q)x + pq leads to the need to determine integers that add to b and have a product c when factoring a trinomial of the form x2 + bx + c.

Again, I know how to apply this question while factoring, but is the correct response to this question that the numbers need to add up correctly? They need to follow a pattern?

Answer 1

Start with the factors:

 

(x + p)(x + q)          Now multiply using FOIL

x² + qx + px + pq    Factor the middle term

x² + (p + q)x + pq

 

So if given, as an example:

x² + 6x + 8          

p + q = 6, and pq = 8

p = 2 and q = 6, they could be the other way around

 

x² + 6x + 8 = (x + 2)(x + 6)

.

They do follow a pattern, FOIL