Answer:
The remainder is 10
Step-by-step explanation:
In division operation
Dividend ÷ divisor = quotient + remainder/divisor
Let us use the remainder Theorem to solve the question
∵ The dividend is [tex]3x^{4}+2x^{3}-x^{2}+2x-14[/tex]
∵ 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
∵ [tex]3(-2)^{4}+2(-2)^{3}-(-2)^{2}+2(-2)-14[/tex] =
3(16) + 2(-8) - (4) - 4 - 14 =
48 - 16 - 4 - 4 - 14 = 10
∴ The remainder is 10
