Question

An expression is shown below:

Answer 1

The factored expression is:

$3y(x^3 + 4x - 3x^2 - 12)$

------------------------

To factor the expression:

• First, we need to find the greatest common factor of the numeric and symbolic coefficients.
• Then, we divide each term of the expression by it's gcf.

------------------------

The expression is:

$3x^3y + 12xy - 9x^2y - 36y$

------------------------

The numeric coefficients are: 3, 12, 9, 36

The gcf of the numeric coefficients is:

3 - 12 - 9 - 36|3

1 - 4 - 3 - 12

The gcf of the numeric coefficients is 3, as 3 is the only number by which 3, 12, 9 and 36 are all divisible.

------------------------

The symbolic coefficients are: $x^3y, xy, x^2y, y$

The only common term is y, so y is the gcf of the symbolic coefficients.

------------------------

The gcf of the entire expression is the multiplication of the gcfs of the numeric and of the symbolic coefficients, so it is 3y.

Now, to factore the expression:

$3x^3y + 12xy - 9x^2y - 36y = 3y(\frac{3x^3y}{3y} + \frac{12xy}{3y} - \frac{9x^2y}{3y} - \frac{36y}{3y}) = 3y(x^3 + 4x - 3x^2 - 12)$

The factored expression is:

$3y(x^3 + 4x - 3x^2 - 12)$

A similar problem is given at brainly.com/question/20691631

Answer 2

Answer:

Part A: so the GCF is 3y, 

We need to rewrite the equation such as: 

-36 as -12 · 3, -9 as -3 · 3, 12 as 4 · 3

It will look like this: 

3x^3 y +4 · 3xy + 3 · 3x^2 y + 4 · 3 · 3y

We then need to factor out 3y:

3y(x^3 + 4x - 3x^2 - 12)

Part b: factor out completely

3y(x^3 + 4x - 3x^2 - 12)

So, we need to do the following:

3y{x^2(x-3) + 4 (x-3)}

we then get the final factor: 3y(x - 3) (x^2 + 4)

Step-by-step explanation: