Question

if x+3 is a a factor of x^3+6x^2+11x+k ,then k =​

Answer 1

Answer:

6

Step-by-step explanation:

x+3 ) x³+6x²+11x+k ( x²+3x+2

- x³+3x²

0 +3x²+11x

- 3x²+9x

0 +2x+k

- 2x+6

0

if reminder is 0, then k = 6

Answer 2

Step-by-step explanation:

$x + 3 = 0 \\ \bf{x ={ \underline{ \underline { - 3}}}} \\ \\ p(x) = {x}^{3} + 6 {x}^{2} + 11x + k = 0 \\ p( - 3) = {( - 3)}^{3} + 6 {( - 3)}^{2} + 11( - 3) + k = 0 \\ = - 27 + 6(9) + ( - 33) + k = 0 \\ = - 27 + 54 - 33 + k = 0\\ = -6 + k = 0 \\ { \bf {k = { \underline{ \underline{6}}}}}$