Please explain to me how to factor x^2+5x-24

Question

solomonzelman · Answer

find 2 numbers that
a)   Add to  5
b)   Multiply to get -24

1)           1 number is negative and the other is positive
2)           The absolute value of the positive number is greater than the absolute value of the negative one, because the sum (i.e the middle term is positive)
3)           the 2 numbers are ± factors of 24, so you have the following options to check.

$$-1~~~~and~~~~24$$$$-2~~~~and~~~~12$$$$-3~~~~and~~~~8$$$$-4~~~~and~~~~6$$

solomonzelman · Answer

Is 5 a difference between any pair of the factors?

solomonzelman · Answer

You can also tell that you can't factor this, because the discriminant   the b²-4(a)(c)   is not a perfect square in this case,

b²-4(a)(c) 
a=1  b=5  c=-24

(5)²-4(1)(-24)
25-(-96)
25+96
131

solomonzelman · Answer

$$144=(±~12)^{2}~~~~~ ──── ~~~~121=(±~11)^2$$