Question

Find the value of k if the remainder is −6 when 2x³ − 6x² + kx + 6 is divided by x + 3.

Answer 1

Let f(x) = 2x³ − 6x² + kx + 6

Now, by the remainder theorem,

f(−3) = −6

Step 1: Substitute x = −3 in f(x)

f(−3) = 2(−3)³ − 6(−3)² + k(−3) + 6

= 2(−27) − 6(9) − 3k + 6

= −54 − 54 − 3k + 6

= −102 − 3k

Step 2: Set equal to the remainder:

−102 − 3k = −6

Step 3: Solve for k:

−102 − 3k = −6

−3k = −6 + 102

−3k = 96

k = `96/-3`

k = −32

∴ The value of k is −32.