Question

Find the value of k if the remainder is 12 when x³ + 4x² − 7x + k is divided by x − 2.

Answer 1

Let f(x) = x³ + 4x² − 7x + k

Now, by the remainder theorem,

f(2) = 12

Step 1: Substitute x = 2 in f(x)

f(2) = 2³ + 4(2)² − 7(2) + k

= 8 + 4(4) − 14 + k

= 8 + 16 − 14 + k

= 10 + k

Step 2: Set equal to the remainder:

10 + k = 12

Step 3: Solve for k:

10 + k = 12

k = 12 − 10

k = 2

∴ The value of k is 2.