The value of k is 8
x + 3 is a factor of P(x) using the factor theorem if P(-3) = 0.
Since P(x) = x³ + 4x² + kx + 15
P(-3) = (-3)³ + 4(-3)² + k(-3) + 15
P(-3) = -27 + 4(9) - 3k + 15
P(-3) = -27 + 36 - 3k + 15
Collecting like terms
P(-3) = 24 - 3k
Since P(-3) = 0, since x + 3 is a factor, we have that
24 - 3k = 0
Adding 3k to both sides, we have
3k = 24
Dividing both sides by 3
k = 24/3
k = 8
So, the value of k is 8
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