Answer :
To divide the polynomial [tex]\(32x^3 + 48x^2 - 40x\)[/tex] by [tex]\(8x\)[/tex], we can perform polynomial division by distributing the division over each term in the polynomial.
1. Divide each term by [tex]\(8x\)[/tex]:
- First, divide the term [tex]\(32x^3\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
\frac{32x^3}{8x} = 4x^2
\][/tex]
- Next, divide the term [tex]\(48x^2\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
\frac{48x^2}{8x} = 6x
\][/tex]
- Finally, divide the term [tex]\(-40x\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
\frac{-40x}{8x} = -5
\][/tex]
2. Combine the results:
Therefore, the result of dividing [tex]\(32x^3 + 48x^2 - 40x\)[/tex] by [tex]\(8x\)[/tex] is:
[tex]\[
4x^2 + 6x - 5
\][/tex]
So, the quotient is [tex]\(4x^2 + 6x - 5\)[/tex] with no remainder.
1. Divide each term by [tex]\(8x\)[/tex]:
- First, divide the term [tex]\(32x^3\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
\frac{32x^3}{8x} = 4x^2
\][/tex]
- Next, divide the term [tex]\(48x^2\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
\frac{48x^2}{8x} = 6x
\][/tex]
- Finally, divide the term [tex]\(-40x\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
\frac{-40x}{8x} = -5
\][/tex]
2. Combine the results:
Therefore, the result of dividing [tex]\(32x^3 + 48x^2 - 40x\)[/tex] by [tex]\(8x\)[/tex] is:
[tex]\[
4x^2 + 6x - 5
\][/tex]
So, the quotient is [tex]\(4x^2 + 6x - 5\)[/tex] with no remainder.
