Answer:
2 • (g - 2) • (4g + 3)
Step-by-step explanation:
Step by Step Solution
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STEP
1
:
Equation at the end of step 1
(23g2 - 10g) - 12
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
8g2 - 10g - 12 = 2 • (4g2 - 5g - 6)
Trying to factor by splitting the middle term
3.2 Factoring 4g2 - 5g - 6
The first term is, 4g2 its coefficient is 4 .
The middle term is, -5g its coefficient is -5 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 4 • -6 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -5 .
-24 + 1 = -23
-12 + 2 = -10
-8 + 3 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 3
4g2 - 8g + 3g - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
4g • (g-2)
Add up the last 2 terms, pulling out common factors :
3 • (g-2)
Step-5 : Add up the four terms of step 4 :
(4g+3) • (g-2)
Which is the desired factorization
Final result :
2 • (g - 2) • (4g + 3)
