Answer:
-x2-10x+24=0
Two solutions were found :
x = 2
x = -12
Step by step solution :
Step 1 :
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
-x2 - 10x + 24 = -1 • (x2 + 10x - 24)
Trying to factor by splitting the middle term
2.2 Factoring x2 + 10x - 24
The first term is, x2 its coefficient is 1 .
The middle term is, +10x its coefficient is 10 .
The last term, "the constant", is -24
Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is 10 .
-24 + 1 = -23
-12 + 2 = -10
-8 + 3 = -5
-6 + 4 = -2
-4 + 6 = 2
-3 + 8 = 5
-2 + 12 = 10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 12
x2 - 2x + 12x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
12 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x+12) • (x-2)
Which is the desired factorization
