Question

divide: \\(dfrac{16x^3 + 12x^2 - 8x}{4x}\\)

Explanation:

Step1: Split the fraction

We can split the given fraction \(\frac{16x^{3}+12x^{2}-8x}{4x}\) into three separate fractions: \(\frac{16x^{3}}{4x}+\frac{12x^{2}}{4x}-\frac{8x}{4x}\)

Step2: Simplify each fraction

• For \(\frac{16x^{3}}{4x}\), divide the coefficients and subtract the exponents of \(x\): \(\frac{16}{4}x^{3 - 1}=4x^{2}\)
• For \(\frac{12x^{2}}{4x}\), divide the coefficients and subtract the exponents of \(x\): \(\frac{12}{4}x^{2 - 1}=3x\)
• For \(\frac{8x}{4x}\), divide the coefficients and subtract the exponents of \(x\) (note the negative sign): \(-\frac{8}{4}x^{1 - 1}=-2\)

Answer:

\(4x^{2}+3x - 2\)