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].
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].
