Answer :
To divide the polynomial [tex]\(32x^3 + 48x^2 - 40x\)[/tex] by [tex]\(8x\)[/tex], you can simplify each term of the polynomial separately. Here's a step-by-step solution:
1. Divide the first term:
[tex]\[
\frac{32x^3}{8x} = 4x^2
\][/tex]
2. Divide the second term:
[tex]\[
\frac{48x^2}{8x} = 6x
\][/tex]
3. Divide the third term:
[tex]\[
\frac{-40x}{8x} = -5
\][/tex]
Now, combine these results to form the quotient:
[tex]\[
4x^2 + 6x - 5
\][/tex]
So, the division of [tex]\(32x^3 + 48x^2 - 40x\)[/tex] by [tex]\(8x\)[/tex] results in the simplified expression:
[tex]\[
4x^2 + 6x - 5
\][/tex]
1. Divide the first term:
[tex]\[
\frac{32x^3}{8x} = 4x^2
\][/tex]
2. Divide the second term:
[tex]\[
\frac{48x^2}{8x} = 6x
\][/tex]
3. Divide the third term:
[tex]\[
\frac{-40x}{8x} = -5
\][/tex]
Now, combine these results to form the quotient:
[tex]\[
4x^2 + 6x - 5
\][/tex]
So, the division of [tex]\(32x^3 + 48x^2 - 40x\)[/tex] by [tex]\(8x\)[/tex] results in the simplified expression:
[tex]\[
4x^2 + 6x - 5
\][/tex]
