Day 4 - Easy Trinomials

 $x^2+3x+2x+6$  

 $x^2+5x+6$  

We are essentially going in reverse

 $x^2+5x+6\ \rightarrow\ \left(x+2\right)\left(x+3\right)$  

What pattern do you notice? (Where do we get the 5 and 6?)

Standard form:  $ax^2+bx+c$  This form will help us understand later when I call terms by 'a, b, and c'.

In the previous problem, we found two numbers that multiplied to our 'c' (6), and added to our 'b' (5)

In this case, what are two numbers that multiply to our 'c' (12), and add to 'b' (7)?

4 & 3, right?

So our two factors would be  $\left(x+4\right)\left(x+3\right)$  (FOIL this back out to check your answer!)

Same method applies - look for factors that multiply to -14, and add to -5. Try this on your own first!

-7, 2 ? ( $-7\cdot2=-14;\ -7+2=-5$  )

 $\left(x-7\right)\left(x+2\right)$