Respuesta :
Answer:
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
((0 - 22x2) - 64x) - 192 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-4x2 - 64x - 192 = -4 • (x2 + 16x + 48)
Trying to factor by splitting the middle term
3.2 Factoring x2 + 16x + 48
The first term is, x2 its coefficient is 1 .
The middle term is, +16x its coefficient is 16 .
The last term, "the constant", is +48
Step-1 : Multiply the coefficient of the first term by the constant 1 • 48 = 48
Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is 16 .
-48 + -1 = -49
-24 + -2 = -26
-16 + -3 = -19
-12 + -4 = -16
-8 + -6 = -14
-6 + -8 = -14
-4 + -12 = -16
-3 + -16 = -19
-2 + -24 = -26
-1 + -48 = -49
1 + 48 = 49
2 + 24 = 26
3 + 16 = 19
4 + 12 = 16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 12
x2 + 4x + 12x + 48
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+4)
Add up the last 2 terms, pulling out common factors :
12 • (x+4)
Step-5 : Add up the four terms of step 4 :
(x+12) • (x+4)
Which is the desired factorization
