Question

question 8 (4 points)

is the following expression equivalent to the function in the previous question? explain and show your work.

\\(\frac{-3x^3 - 10x^2 + 9x + 4}{6x^3 - 33x^2 + 15x}\\)

Explanation:

Expand the simplified expression

$$
LATEXBLOCK0
$$

Compare with the given expression

$$
LATEXBLOCK1
$$

State the conclusion

$$ \text{The expressions are not equivalent because their denominators differ.} $$

Answer:

No, the expression is not equivalent to the simplified function shown in the work.

When expanding the simplified expression:

• The numerator is \(-(x-1)(x+4)(3x+1) = -3x^3 - 10x^2 + 9x + 4\), which matches the given expression's numerator.
• The denominator is \(3x(x-5)(2x+1) = 6x^3 - 27x^2 - 15x\), which does not match the given expression's denominator of \(6x^3 - 33x^2 + 15x\).