Polynomial Remainders and Evaluations

x^3 + kx^2 + 17x - 6

x^3 - kx^2 + 17x + 6

x^3 + kx^2 - 17x + 6

x^3 - kx^2 - 17x - 6

6

12

18

24

Find the value of K

Find the remainder when P(x) is divided by x - 3

Find the remainder when P(x) is divided by 3x + 2

Simplify the polynomial

By setting P(-3) equal to 12 and solving for K

By setting P(0) equal to 12 and solving for K

By setting P(1) equal to 12 and solving for K

By setting P(3) equal to 12 and solving for K

9

7

6

8

27 - 9K + 51 + 6

27 + 9K - 51 + 6

27 - 9K - 51 - 6

27 + 9K + 51 - 6

12

24

36

48

Simplify the expression

Verify with a calculator

Find P(-2/3)

Solve for K

Substitute K into the polynomial and find P(-3)

Substitute K into the polynomial and find P(3)

Substitute K into the polynomial and find P(-2/3)

Substitute K into the polynomial and find P(2/3)

-2/3^3 - 8(-2/3)^2 - 17(-2/3) + 6

-2/3^3 + 8(-2/3)^2 - 17(-2/3) + 6

-2/3^3 + 8(-2/3)^2 + 17(-2/3) + 6

-2/3^3 - 8(-2/3)^2 + 17(-2/3) + 6