What is the remainder when (2x3 + 4x2 - 32x + 18) ÷ (x - 3)?
Solution:
Given, (2x3 + 4x2 - 32x + 18) ÷ (x - 3)
We have to find the remainder.
By long division,
Therefore, the remainder is 12.
Alternate method -
The remainder theorem is stated as follows: When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k).
Using the remainder theorem
x = 3
Substituting it we get
f(3) = 2(3)3 + 4(3)2 - 32(3) + 18
f(3) = 2(27) + 4 (9) - 32 (3) + 18
So we get
f(3) = 54 + 36 - 96 + 18
f(3) = 12
Therefore, the remainder is 12.
What is the remainder when (2x3 + 4x2 - 32x + 18) ÷ (x - 3)?
Summary:
The remainder when (2x3 + 4x2 - 32x + 18) ÷ (x - 3) is 12.