Question

What is the reminder when (3x^4+2x^3-x^2+2x-14) divided by (x+2)

Answer 1

The remainder is 10

Explanation:

In division operation

Dividend ÷ divisor = quotient + remainder/divisor

Let us use the remainder Theorem to solve the question

• If the divisor is x + a equate it by zero to find the value of x (x = -a)
• Substitute x in the dividend by this value and calculate it
• The answer of the dividend is the remainder

∵ The dividend is
`3x^(4)+2x^(3)-x^(2)+2x-14`

∵ The divisor is (x + 2)

- Equate the divisor by 0 to find the value of x

∵ x + 2 = 0

- Subtract 2 from both sides

∴ x = -2

Substitute each x in the dividend by -2 and find its value

∵
`3(-2)^(4)+2(-2)^(3)-(-2)^(2)+2(-2)-14` =

3(16) + 2(-8) - (4) - 4 - 14 =

48 - 16 - 4 - 4 - 14 = 10

∴ The remainder is 10