Question

12x^4 − 20x^2+ 32x

Answer 1

1) common factors of the variable is x

2) common factors of the constants is 4

3) common factors of the expression is 4x

Solution:

Given that,

$12x^4 - 20x^2 + 32x$

1. Explain how you find the common factors of the variable?

The variables are:

$x^4\\\\x^2\\\\x$

Find the factors:

$x^4 = x \times x \times x \times x\\\\x^2 = x \times x\\\\x$

Here, "x" is present in all variables

x is the greatest common factor

Thus common factors of the variable is x

2, Explain how you find the common factors of the constants?

The constants are 12, 20 and 32

Find the greatest common factor

List down factors of 12, 20 and 32

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 32 are: 1, 2, 4, 8, 16, 32

Then the greatest common factor is 4

The common factors of the constants is 4

3. What are the common factors of the expression?

Given is:

$12x^4 - 20x^2 + 32x$

Factor out x and 4

$4x(3x^3 - 5x + 8)$

The common factors of the expression is 4x