Simplify the expression completely if possible. (x^(4)-8x^(3))/(x^(2)-5x-24) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator if possible. The numerator is x^4 - 8x^3, which can be factored by taking out the common factor x^3, resulting in x^3(x - 8). The denominator is a quadratic expression x^2 - 5x - 24, which can be factored into (x - 8)(x + 3) because (-8) * (+3) = -24 and (-8) + (+3) = -5. So, the expression becomes (x^3(x - 8))/(x - 8)(x + 3).Cancel Common Factors: Cancel out the common factors. The factor (x - 8) is present in both the numerator and the denominator, so we can cancel it out. This gives us x^3/(x + 3).Check Further Simplification: Check for any further simplification. There are no common factors left in the numerator and the denominator, and no further simplification is possible. So, the simplified expression is x^3/(x + 3).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the expression completely if possible.

(x^(4)-8x^(3))/(x^(2)-5x-24)
Answer:

Simplify the expression completely if possible. $\newline$ $\frac{x^{4}-8 x^{3}}{x^{2}-5 x-24}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Simplify the expression completely if possible.

\newline

\frac{x^{4}-8 x^{3}}{x^{2}-5 x-24}

\newline

Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator if possible. $\newline$ The numerator is $x^4 - 8x^3$ , which can be factored by taking out the common factor $x^3$ , resulting in $x^3(x - 8)$ . $\newline$ The denominator is a quadratic expression $x^2 - 5x - 24$ , which can be factored into $(x - 8)(x + 3)$ because $(-8) \times (+3) = -24$ and $(-8) + (+3) = -5$ . $\newline$ So, the expression becomes $(x^3(x - 8))/(x - 8)(x + 3)$ .
Cancel Common Factors: Cancel out the common factors. $\newline$ The factor $(x - 8)$ is present in both the numerator and the denominator, so we can cancel it out. $\newline$ This gives us $\frac{x^3}{x + 3}$ .
Check Further Simplification: Check for any further simplification. $\newline$ There are no common factors left in the numerator and the denominator, and no further simplification is possible. $\newline$ So, the simplified expression is $x^3/(x + 3)$ .