Answer :

To solve the expression [tex]\(25x^3 + 30x^2 - 40x\)[/tex], we can follow these steps to factor it:

1. Identify the Common Factor:
Look at each term in the expression: [tex]\(25x^3\)[/tex], [tex]\(30x^2\)[/tex], and [tex]\(-40x\)[/tex]. Notice that each term contains the variable [tex]\(x\)[/tex], and they all include coefficients that share a common factor. The greatest common factor (GCF) of the numerical coefficients (25, 30, 40) is 5.

2. Factor Out the Common Term:
Since each term has at least one [tex]\(x\)[/tex], we can factor out [tex]\(5x\)[/tex] from the expression. This means we will divide each term by [tex]\(5x\)[/tex]:

- Divide [tex]\(25x^3\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
\frac{25x^3}{5x} = 5x^2
\][/tex]

- Divide [tex]\(30x^2\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
\frac{30x^2}{5x} = 6x
\][/tex]

- Divide [tex]\(-40x\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
\frac{-40x}{5x} = -8
\][/tex]

So, factoring [tex]\(5x\)[/tex] from the entire expression gives us:
[tex]\[
25x^3 + 30x^2 - 40x = 5x(5x^2 + 6x - 8)
\][/tex]

3. Result:
The factored form of the original expression is [tex]\(5x(5x^2 + 6x - 8)\)[/tex].

Therefore, the solution to the expression [tex]\(25x^3 + 30x^2 - 40x\)[/tex] is that it can be factored as [tex]\(5x(5x^2 + 6x - 8)\)[/tex].

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