Answer :

To factor the expression [tex]\(5x^3 + 25x^2 - 70x\)[/tex] completely, we can follow these steps:

1. Look for a common factor in all terms:

Each term in the expression [tex]\(5x^3 + 25x^2 - 70x\)[/tex] has a common factor of [tex]\(5x\)[/tex]. Let's factor out [tex]\(5x\)[/tex] from each term:

[tex]\[
5x(x^2 + 5x - 14)
\][/tex]

2. Factor the quadratic expression:

Next, we need to factor the quadratic part, [tex]\(x^2 + 5x - 14\)[/tex]. We look for two numbers that multiply to [tex]\(-14\)[/tex] (the constant term) and add to [tex]\(5\)[/tex] (the linear coefficient).

The working numbers are [tex]\(7\)[/tex] and [tex]\(-2\)[/tex], since [tex]\(7 \times (-2) = -14\)[/tex] and [tex]\(7 + (-2) = 5\)[/tex].

3. Express the quadratic as a product of binomials:

Using these numbers, we can write the quadratic expression as:

[tex]\[
x^2 + 5x - 14 = (x + 7)(x - 2)
\][/tex]

4. Combine everything:

Substituting back into the expression where we factored out [tex]\(5x\)[/tex]:

[tex]\[
5x(x + 7)(x - 2)
\][/tex]

Therefore, the completely factored form of the expression [tex]\(5x^3 + 25x^2 - 70x\)[/tex] is:

[tex]\[
5x(x - 2)(x + 7)
\][/tex]

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Rewritten by : Barada