Answer :
Sure! Let's solve this problem step-by-step:
We are asked to find the quotient of the expression:
[tex]\[
\frac{35x^5 - 20x^4 + 45x^3}{5x^2}
\][/tex]
Step 1: Break down the division
Each term in the numerator should be divided by the term in the denominator [tex]\(5x^2\)[/tex].
Step 2: Divide each term individually
1. [tex]\( \frac{35x^5}{5x^2} \)[/tex]
Divide the coefficients: [tex]\( \frac{35}{5} = 7 \)[/tex].
Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(5 - 2 = 3\)[/tex].
The result is: [tex]\(7x^3\)[/tex].
2. [tex]\( \frac{-20x^4}{5x^2} \)[/tex]
Divide the coefficients: [tex]\( \frac{-20}{5} = -4 \)[/tex].
Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(4 - 2 = 2\)[/tex].
The result is: [tex]\(-4x^2\)[/tex].
3. [tex]\( \frac{45x^3}{5x^2} \)[/tex]
Divide the coefficients: [tex]\( \frac{45}{5} = 9 \)[/tex].
Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(3 - 2 = 1\)[/tex].
The result is: [tex]\(9x\)[/tex].
Step 3: Combine the results
Combine all the terms from Step 2 to write the complete answer:
[tex]\[
7x^3 - 4x^2 + 9x
\][/tex]
So, the quotient of the given expression is [tex]\( 7x^3 - 4x^2 + 9x \)[/tex].
We are asked to find the quotient of the expression:
[tex]\[
\frac{35x^5 - 20x^4 + 45x^3}{5x^2}
\][/tex]
Step 1: Break down the division
Each term in the numerator should be divided by the term in the denominator [tex]\(5x^2\)[/tex].
Step 2: Divide each term individually
1. [tex]\( \frac{35x^5}{5x^2} \)[/tex]
Divide the coefficients: [tex]\( \frac{35}{5} = 7 \)[/tex].
Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(5 - 2 = 3\)[/tex].
The result is: [tex]\(7x^3\)[/tex].
2. [tex]\( \frac{-20x^4}{5x^2} \)[/tex]
Divide the coefficients: [tex]\( \frac{-20}{5} = -4 \)[/tex].
Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(4 - 2 = 2\)[/tex].
The result is: [tex]\(-4x^2\)[/tex].
3. [tex]\( \frac{45x^3}{5x^2} \)[/tex]
Divide the coefficients: [tex]\( \frac{45}{5} = 9 \)[/tex].
Subtract the exponents of [tex]\(x\)[/tex]: [tex]\(3 - 2 = 1\)[/tex].
The result is: [tex]\(9x\)[/tex].
Step 3: Combine the results
Combine all the terms from Step 2 to write the complete answer:
[tex]\[
7x^3 - 4x^2 + 9x
\][/tex]
So, the quotient of the given expression is [tex]\( 7x^3 - 4x^2 + 9x \)[/tex].
