x^4 + 2x^3 -29x^2 -47x+77 all divided by x^2 -2x -15

asked by guest
on Sep 22, 2024 at 2:12 am



You asked:

Evaluate the expression: \(\frac{{x}^{4} + 2 \cdot {x}^{3} - 29 \cdot {x}^{2} - 47 x + 77}{{x}^{2} - 2 x - 15}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{{x}^{4} + 2 \cdot {x}^{3} - 29 \cdot {x}^{2} - 47 x + 77}{{x}^{2} - 2 x - 15} = \frac{x^{4} + 2 x^{3} - 29 x^{2} - 47 x + 77}{x^{2} - 2 x - 15} \)

Expanded

\[\frac{{x}^{4} + 2 \cdot {x}^{3} - 29 \cdot {x}^{2} - 47 x + 77}{{x}^{2} - 2 x - 15} = \frac{x^{4}}{x^{2} - 2 x - 15} + \frac{2 x^{3}}{x^{2} - 2 x - 15} - \frac{29 x^{2}}{x^{2} - 2 x - 15} - \frac{47 x}{x^{2} - 2 x - 15} + \frac{77}{x^{2} - 2 x - 15}\]

Factored

\[\frac{{x}^{4} + 2 \cdot {x}^{3} - 29 \cdot {x}^{2} - 47 x + 77}{{x}^{2} - 2 x - 15} = \frac{x^{4} + 2 x^{3} - 29 x^{2} - 47 x + 77}{\left(x - 5\right) \left(x + 3\right)}\]

+ Submit Question