Answer :

To simplify the expression [tex]\(\frac{32x^3 + 48x^2 - 80x}{8x}\)[/tex], we'll follow these steps:

1. Factor the Numerator:
The numerator is [tex]\(32x^3 + 48x^2 - 80x\)[/tex]. Notice that each term has a common factor of [tex]\(16x\)[/tex]. So, we can factor out [tex]\(16x\)[/tex]:

[tex]\[
32x^3 + 48x^2 - 80x = 16x(2x^2 + 3x - 5)
\][/tex]

2. Rewrite the Expression:
Substitute the factored form back into the expression:

[tex]\[
\frac{16x(2x^2 + 3x - 5)}{8x}
\][/tex]

3. Cancel Out Common Factors:
The common factor in both the numerator and the denominator is [tex]\(8x\)[/tex]. Simplifying, we get:

[tex]\[
\frac{16x}{8x} \cdot (2x^2 + 3x - 5) = 2 \cdot (2x^2 + 3x - 5)
\][/tex]

Simplifying further gives us:

[tex]\[
4x^2 + 6x - 10
\][/tex]

Therefore, the simplified expression is [tex]\(4x^2 + 6x - 10\)[/tex].

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