Question

if x+6 is a factor of p (x) =x³+3x2+4x+k find the value of K

Answer 1

Hey mate!!

✴FACTOR THEOREM✴

p(x) = x³ + 3x² + 4x + k

g(x) = x + 6 = 0

=> x = -6

p(-6) = (-6)³ + 3(-6)² + 4(-6) + k

p(-6) = -216 + 108 - 24 + k

p(-6) = -240 + 108 + k

p(-6) = - 132 + k

$\therefore$ -132 + k = 0

=> k = 132


Thanks for the question!!

☺☺☺

Answer 2

As we know x+6 is a factor of p(x). Then, x+6=0. Hence, X= -6.

Replace the value in p(x). We get....

(-6)^3 + 3(-6)^2 + 4(-6) +k = 0

-216 + 108 -24 + k = 0

-132 + k =0

k=132

Hope that helped you !