College

What is the quotient of the following?

\[ \frac{35x^5 - 20x^4 + 45x^3}{5x^2} \]

A. \(\square\) \(x\)

B. \(\square - \square\)

C. \(\square\)

D. \(\square\) \(x\)

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].