2k^2-13k-24
Factor the expression..
(2k+3)(k-8)
To factor the expression 2k^2 - 13k - 24, we need to find two numbers whose product is equal to the product of the coefficient of the squared term (2) and the constant term (-24) and whose sum is equal to the coefficient of the linear term (-13).
The product of 2 and -24 is -48, so we need to find two numbers whose product is -48 and whose sum is -13.
Possible pairs of numbers whose product is -48 are:
1 and -48
-1 and 48
2 and -24
-2 and 24
3 and -16
-3 and 16
4 and -12
-4 and 12
6 and -8
-6 and 8
Among these pairs, the pair whose sum is -13 is -1 and 24.
Therefore, we can factor the expression as follows:
2k^2 - 13k - 24 = (2k + 1)(k - 24)