Question

use factoring to find the following quotient n^2-15n+56÷n-8 a)n-7 b) n-10+ 2/n-8 c)n-5+ 2/n-8 d) n-7+ 5/n-8

Answer 1

`(n^2-15n+56)/(n-8)`

Factoring the numerator

`n^2-15n+56=0`

use the formula

`n=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

and replace

`\begin{gathered} n=\frac{-(-15)\pm\sqrt[]{(-15)^2-4(1)(56)}}{2(1)} \\ \\ n=\frac{15\pm\sqrt[]{1}}{2} \\ \\ n=(15\pm1)/(2) \\ \\ n_1=(15+1)/(2)=8 \\ \\ n_2=(15-1)/(2)=7 \end{gathered}`

the factored expression is

`(n-8)(n-7)`

now replacing on the first expression

`((n-8)(n-7))/((n-8))`

we can simplify (n-8),so

`((n-8)(n-7))/((n-8))\longrightarrow(n-7)`

so, the right option is A