Answer:
[tex]k = -20[/tex]
Step-by-step explanation:
According to the Remainder Theorem if you divide any polynomial, [tex]P(x)[/tex], by [tex]D(x) = x -\blue{a}[/tex], the remainder is [tex]P(\blue{a})[/tex].
If you want [tex]f(x)[/tex] to have a remainder of [tex]70[/tex] when we divide it by [tex]x -\blue{9}[/tex], we are essentially solving for [tex]f(\blue{9}) = 70[/tex]
[tex]f(9) = 70 \\ (9)^2 +(9) +k = 70 \\ 81 +9 +k = 70 \\ k = 70 -81 -9 \\ k = -20 [/tex]
