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10-07-2022
Mathematics

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Find the value of p.

Find the value of p class=

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fieryanswererft fieryanswererft

10-07-2022

Answer:

p = 9

Explanation:

There is no remainder when a polynomial is completely divided by divisor.

Here:

divisor: (x - 6)

polynomial: f(x) = x³ - 13x² + 6px - 72

Set to zero:

(x - 6) = 0

x = 6

Insert into equation.

f(6) = 0

(6)³ - 13(6)² + 6p(6) - 72 = 0

216 - 468 + 36p - 72 = 0

-324 + 36p = 0

36p = 324

p = 324/36

p = 9

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