You also may use the alternative method of solving , hence, using the reminder theorem yields:
`x^3 + 3x^2 - kx + 10 = (x - 5)(ax^2 + bx + c) + 15`
Using the undetermined coefficients method, you need to evaluate `a,b,c,` equating the coefficients of like powers, such that:
`x^3 + 3x^2 - kx + 10 = ax^3 + bx^2 + cx - 5ax^2 - 5bx - 5c + 15`
`x^3 + 3x^2 - kx + 10 = x^3 + x^2(b - 5a) + x(c - 5b) + 15 - 5c`
`a = 1`
`b - 5a = 3 => b - 5 = 3 => b = 8`
`15 - 5c = 10 => -5c = 10 - 15 => -5c = -5 => c = 1`
`c - 5b = -k => 1 - 40 = -k => k = 39`
Hence, evaluating k under the given conditions yields `k = 39` , hence, you need to select the valid answer `b) 39` .
`f(x)=x^3+3x^2-x+10` ,when f(x) divided by x-5 ,remainder will be f(5).
But remainder f(5)=15
Thus correct answer is b