Question

find the value of the given expression: 6a^3 - 4a^2 + 1/8 for a= -1/2​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((6 • (a3)) - (2•32a2)) - 24a

STEP

2

:

Equation at the end of step

2

:

((2•3a3) - (2•32a2)) - 24a

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

6a3 - 18a2 - 24a = 6a • (a2 - 3a - 4)

Trying to factor by splitting the middle term

4.2 Factoring a2 - 3a - 4

The first term is, a2 its coefficient is 1 .

The middle term is, -3a its coefficient is -3 .

The last term, "the constant", is -4

Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4

Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .

-4 + 1 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1

a2 - 4a + 1a - 4

Step-4 : Add up the first 2 terms, pulling out like factors :

a • (a-4)

Add up the last 2 terms, pulling out common factors :

1 • (a-4)

Step-5 : Add up the four terms of step 4 :

(a+1) • (a-4)

Which is the desired factorization

Final result :

6a • (a + 1) • (a - 4)