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chibabykalu16

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)

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