What is the right choice for question 22) ?

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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` .**

Let

`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

`5^3+3xx5^2-5k+10=15`

`125+75-5k+10=15`

`-5k=-195`

`k=39`

**Thus correct answer is b**

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