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Answer :
To divide [tex]\((-25x^3 + 45x^2 - 40x)\)[/tex] by [tex]\(5x\)[/tex], you can follow these steps:
1. Divide each term separately:
- Start by dividing the first term in the numerator [tex]\(-25x^3\)[/tex] by the divisor [tex]\(5x\)[/tex]:
[tex]\[
\frac{-25x^3}{5x} = -5x^2
\][/tex]
- Next, divide the second term [tex]\(45x^2\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
\frac{45x^2}{5x} = 9x
\][/tex]
- Finally, divide the third term [tex]\(-40x\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
\frac{-40x}{5x} = -8
\][/tex]
2. Combine the results:
- After dividing each term individually by [tex]\(5x\)[/tex], combine the results to form the quotient:
[tex]\[
-5x^2 + 9x - 8
\][/tex]
3. Check for any remainder:
- Since all terms were divided evenly by the divisor with no leftovers, the remainder is 0.
Thus, the division of [tex]\((-25x^3 + 45x^2 - 40x)\)[/tex] by [tex]\(5x\)[/tex] results in a quotient of [tex]\(-5x^2 + 9x - 8\)[/tex], with no remainder.
1. Divide each term separately:
- Start by dividing the first term in the numerator [tex]\(-25x^3\)[/tex] by the divisor [tex]\(5x\)[/tex]:
[tex]\[
\frac{-25x^3}{5x} = -5x^2
\][/tex]
- Next, divide the second term [tex]\(45x^2\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
\frac{45x^2}{5x} = 9x
\][/tex]
- Finally, divide the third term [tex]\(-40x\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
\frac{-40x}{5x} = -8
\][/tex]
2. Combine the results:
- After dividing each term individually by [tex]\(5x\)[/tex], combine the results to form the quotient:
[tex]\[
-5x^2 + 9x - 8
\][/tex]
3. Check for any remainder:
- Since all terms were divided evenly by the divisor with no leftovers, the remainder is 0.
Thus, the division of [tex]\((-25x^3 + 45x^2 - 40x)\)[/tex] by [tex]\(5x\)[/tex] results in a quotient of [tex]\(-5x^2 + 9x - 8\)[/tex], with no remainder.
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