Question

for what the value of p, x³-3x²+px-6 is divisible by x-3​

Answer 1

Explanation:

Let x-3 be g(x) and x^3 - 3x^2 + px - 6 be f(x).

Zero of g(x) is 3.

By the remainder theorem, if f(3) = 0, f(x) is divisible by g(x).

f(3) = 3^3 - 3(3) ^2 + 3p - 6

     = 27 - 27 + 3p -6

     = 3p - 6

For finding p, f(3) has to be 0.

Hence,

3p - 6 = 0

3p = 6

p = 6/3

p = 2

Answer: p = 2

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