x^2 - 6x + 5, x^2 - 3x - 10
MathBot Answer:
The sum of \({x}^{2} - 6 x + 5\) and \({x}^{2} - 3 x - 10\) is:
\[\begin{aligned}&=\left({x}^{2} - 6 x + 5\right) + \left({x}^{2} - 3 x - 10\right) \\\\ &= 2 x^{2} - 6 x - 3 x - 5 \\\\ &= 2 x^{2} - 9 x - 5 \\\\\end{aligned}\]
The difference of \({x}^{2} - 6 x + 5\) and \({x}^{2} - 3 x - 10\) is:
\[\begin{aligned}&=\left({x}^{2} - 6 x + 5\right) - \left({x}^{2} - 3 x - 10\right) \\\\ &= \left(-1\right) 6 x + 3 x + 15 \\\\ &= 15 - 3 x \\\\\end{aligned}\]
The product of \({x}^{2} - 6 x + 5\) and \({x}^{2} - 3 x - 10\) is:
\[\begin{aligned}&=\left({x}^{2} - 6 x + 5\right) \cdot \left({x}^{2} - 3 x - 10\right) \\\\ &= \left(x^{2} - 3 x - 10\right) \left(x^{2} - 6 x + 5\right) \\\\ &= x^{4} - 9 x^{3} + 13 x^{2} + 45 x - 50 \\\\\end{aligned}\]
The quotient of \({x}^{2} - 6 x + 5\) and \({x}^{2} - 3 x - 10\) is:
\[\begin{aligned}&= \frac{\left({x}^{2} - 6 x + 5\right)}{\left({x}^{2} - 3 x - 10\right)} \\\\ &= \frac{x^{2} - 6 x + 5}{x^{2} - 3 x - 10} \\\\ &= \frac{x - 1}{x + 2} \\\\\end{aligned}\]