What is the right choice for question 6) ?
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It is divided by `x-5`
Therefore, the right option is a).
You may use as alternative method, the reminder theorem, such that:
`x^3 + 3x^2 - kx + 10 = (x - 5)(ax^2 + bx + c) + 15`
You need to notice that the quotient is second order polynomial whose coefficents are a,b,c.
`x^3 + 3x^2 - kx + 10 = ax^3 + bx^2 + cx - 5ax^2 - 5bx - 5c + 15`
Grouping the terms yields:
`x^3 + 3x^2 - kx + 10 = ax^3 + x^2(b - 5a) + x(c - 5b) - 5c + 15`
Equating the coefficients of like powers yields:
`a = 18`
`b - 5a = 3 => b - 5 = 3 => b = 8`
`15 - 5c = 10 => -5c = -5 => c = 1`
`c - 5b = -k => 1 - 40 = -k => -39 = -k => k = 39`
Hence, evaluating k, using the reminder theorem, yields `k = 39.`
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