Question

Divide:

(-4 x² y³ + 6 x³ y² - 12 x² y²) ÷ (2 x² y²)

Answer 1

Answer:

3x - 2y - 6

Step-by-step explanation:

STEP 1:

Equation at the end of step 1

STEP 2 :

Equation at the end of step2:

 

STEP 3 :

Equation at the end of step3:

 

STEP 4:

Equation at the end of step4:

 

STEP 5:

           6x3y2 - 4x2y3 - 12x2y2

Simplify   ——————————————————————

                   2x2y2        

STEP 6:

Pulling out like terms

6.1     Pull out like factors :

  6x3y2 - 4x2y3 - 12x2y2  =   2x2y2 • (3x - 2y - 6)

Canceling Out :

6.2    Canceling out x2 as it appears on both sides of the fraction line

Canceling Out :

6.3    Canceling out y2 as it appears on both sides of the fraction line

Canceling Out:

6.4      Canceling out  2  as it appears on both sides of the fraction line

Answer 2

o divide the two polynomials, we can use the long division method.

First, we divide the coefficient of the first term of the numerator by the coefficient of the denominator, which is -2. This gives us:

2

Next, we multiply the denominator by 2 and write the result under the first term of the numerator.

(-4 x² y³ + 6 x³ y² - 12 x² y²) ÷ (2 x² y²)

= 2

2 x² y² * 2

(-8 x² y² + 6 x³ y² - 12 x² y²)

We then subtract this result from the numerator:

(-4 x² y³ + 6 x³ y² - 12 x² y²) ÷ (2 x² y²)

= 2

2 x² y² * 2

(-8 x² y² + 6 x³ y² - 12 x² y²)

-(-8 x² y² + 6 x³ y² - 12 x² y²)

    -4 x² y³ + 12 x³ y²

Continuing this process, we eventually get:

(-4 x² y³ + 6 x³ y² - 12 x² y²) ÷ (2 x² y²) = 2 - 2 x + 2 x³

So the answer is 2 - 2 x + 2 x³.