Use the end behavior of the graph to solve 3x^3+9x^2-12x<0

STEP

1

:

Equation at the end of step 1

 ((3 • (x3)) -  32x2) -  12x  = 0

STEP

2

:

Equation at the end of step

2

:

 (3x3 -  32x2) -  12x  = 0

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  3x3 - 9x2 - 12x  =   3x • (x2 - 3x - 4)

Trying to factor by splitting the middle term

4.2     Factoring  x2 - 3x - 4

The first term is,  x2  its coefficient is  1 .

The middle term is,  -3x  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

                    x2 - 4x + 1x - 4

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 :

                    1 • (x-4)

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

                   (x+1)  •  (x-4)

            Which is the desired factorization

Equation at the end of step

4

:

 3x • (x + 1) • (x - 4)  = 0

STEP

5

:

Theory - Roots of a product

5.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Step-by-step explanation:

I hope this helps

6^2 or 36

step-by-step explanation:

6000n

6×1000n

6×10^3 n

so we need 6n need to be a perfect cube

so n has to be 6^2 so that 6n is 6^3

what i'm saying is if you let n be 6^2 you have 6^3×10^3 or 60^3 which is a perfect cube