How do you factor the trinomial # x^2 - 7x + 12#?

2 Answers
Apr 6, 2018

#(x-3)(x-4)#

Here's how I did it:

Explanation:

Two factor a trinomial in form #ax^2 + bx + c#, you must find two numbers that:
#color(red)ax^2 + color(magenta)bx^2+color(blue)c#

  • Multiply up to #color(red)acolor(blue)c#
  • Add up to #color(magenta)b#

In this question, that means the two numbers must:

  • Multiply up to #(color(red)1)(color(blue)12) = 12#
  • Add up to #color(magenta)(-7)#

These two numbers are #-3# and #-4#:
#-3 * -4 = 12#
#-3 -4 = -7#

So now we put them into factored form:
#(x-3)(x-4)#

Hope this helps!

Apr 6, 2018

The factors always multiply to C (12) and add to Bx (7x).
In this case, the answer is (x-4)(x-3) because multiplying two negatives equal a positive and adding two negatives are still negative.