Question

Given f(x)=x^3+9x+kf(x)=x 3 +9x+k, and x-1x−1 is a factor of f(x)f(x), then what is the value of kk?

Answer 1

The factors of a polynomial are the zeros of the polynomial

The value of k is -10

The polynomial function is given as:

$f(x) =x^3 + 9x + k$

x -1 is a factor.

So, we start by writing the factor as an equation

$x -1 = 0$

Add 1 to both sides

$x =1$

Substitute 1 for x in f(x)

$f(1) =1^3 + 9(1) + k$

$f(1) =1 + 9 + k$

Add 1 and 9

$f(1) =10 + k$

Set f(1) to 0, because x - 1 is a factor

$10 + k = 0$

Subtract 10 from both sides

$k = -10$

Hence, the value of k is -10

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