What are all the possible factors of the quadratic term for x²+10x-24? x and x, 10 and x, -24 and 1, -2 and 12

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Answer 1 · 2018-03-29T21:42:25

#-2 and 12#

#x^2+10x-24=(x-2)(x+12)#

.

You have to test all the number pairs that when multiplied together result in #-24#.

If this quadratic is factorable then there is one pair that if you add them together algebraically the result will be #10#.

#24# can be:

#1*24, 2*12, 3*8, 4*6#

But because there is minus sign behind #24#, it means one or the other of the correct pair is negative and the other is positive.

Examining the different pairs, we find that #-2# and #12# are the correct pair because:

#(-2)*12=-24#

#-2+12=10#

#x^2+10x-24=(x-2)(x+12)#