Question

unit 7 review assignment
topic 2: simplifying polynomials

1. \\(\frac{24x^3 - 42x^2 - 6x}{6x}\\)

Explanation:

Step1: Split the fraction

We can split the given fraction \(\frac{24x^{3}-42x^{2}-6x}{6x}\) into three separate fractions: \(\frac{24x^{3}}{6x}-\frac{42x^{2}}{6x}-\frac{6x}{6x}\).

Step2: Simplify each fraction

• For \(\frac{24x^{3}}{6x}\), divide the coefficients and subtract the exponents of \(x\): \( \frac{24}{6}x^{3 - 1}=4x^{2}\).
• For \(\frac{42x^{2}}{6x}\), divide the coefficients and subtract the exponents of \(x\): \( \frac{42}{6}x^{2 - 1}=7x\).
• For \(\frac{6x}{6x}\), the numerator and denominator are equal, so it simplifies to \(1\).

Answer:

\(4x^{2}-7x - 1\)