Question

Write the difference in factored form. (24x4 - 15x2 + 6x) - (10x4 + 5x2 - 4x)​

Answer 1

The factored difference is:
`2x(7x^3 - 10x + 5)`

Explanation:

Difference in non factored form:

To find the difference in non-factored form, we subtract the common terms. So

`24x^4 - 15x^2 + 6x - (10x^4 + 5x^2 - 4x) = 24x^4 - 10x^4 - 15x^2 - 5x^2 + 6x + 4x = 14x^4 - 20x^2 + 10x`

Greatest common factor:

Of the exponents: Between
`x^4, x^2` and
`x`, it is the one with the lowest exponent, so x.

Between 14, 20 and 10:

14 - 20 - 10|2

7 - 10 - 5

So 2

The gcf is 2x, which means that the factored expression is:

`2x((14x^4)/(2x) - (20x^2)/(2x) + (10x)/(2x)) = 2x(7x^3 - 10x + 5)`

The factored difference is:
`2x(7x^3 - 10x + 5)`