Answer:
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Step by Step Solution
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STEP
1
:
Equation at the end of step 1
((0 - (22•3x2)) - 22x) - 8
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-12x2 - 22x - 8 = -2 • (6x2 + 11x + 4)
Trying to factor by splitting the middle term
3.2 Factoring 6x2 + 11x + 4
The first term is, 6x2 its coefficient is 6 .
The middle term is, +11x its coefficient is 11 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 6 • 4 = 24
Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is 11 .
-24 + -1 = -25
-12 + -2 = -14
-8 + -3 = -11
-6 + -4 = -10
-4 + -6 = -10
-3 + -8 = -11
-2 + -12 = -14
-1 + -24 = -25
1 + 24 = 25
2 + 12 = 14
3 + 8 = 11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 8
6x2 + 3x + 8x + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x+1)
Add up the last 2 terms, pulling out common factors :
4 • (2x+1)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (2x+1)
Which is the desired factorization
Final result :
-2 • (2x + 1) • (3x + 4)
Step-by-step explanation:
