Question

find the quotient.
\\(\frac{-56x^4 - 14x^3 - 63x}{7x}\\)
enter the correct answer.

Explanation:

Step1: Divide each term by \(7x\)

We have the numerator \(-56x^4 - 14x^3 - 63x\) and the denominator \(7x\). We will divide each term in the numerator by the denominator.
For the first term: \(\frac{-56x^4}{7x}\)
For the second term: \(\frac{-14x^3}{7x}\)
For the third term: \(\frac{-63x}{7x}\)

Step2: Simplify each term

• Simplify \(\frac{-56x^4}{7x}\):

We can divide the coefficients and subtract the exponents of \(x\) (using the rule \(\frac{x^a}{x^b}=x^{a - b}\)).
The coefficient: \(\frac{-56}{7}=-8\)
The exponent of \(x\): \(x^{4-1}=x^3\)
So, \(\frac{-56x^4}{7x}=-8x^3\)

• Simplify \(\frac{-14x^3}{7x}\):

Coefficient: \(\frac{-14}{7}=-2\)
Exponent of \(x\): \(x^{3 - 1}=x^2\)
So, \(\frac{-14x^3}{7x}=-2x^2\)

• Simplify \(\frac{-63x}{7x}\):

Coefficient: \(\frac{-63}{7}=-9\)
Exponent of \(x\): \(x^{1-1}=x^0 = 1\) (so the \(x\) terms cancel out)
So, \(\frac{-63x}{7x}=-9\)

Step3: Combine the simplified terms

Now we combine the three simplified terms: \(-8x^3-2x^2 - 9\)

Answer:

\(-8x^3-2x^2 - 9\)