P (x) = 2x^4-x^3+2x^2-6. What is the remainder when P (x) is divided by (x-2) ?

Answer: 26

Step-by-step explanation: From the remainder theorem,

If P (x) = 2x⁴ ⁻ x³ + 2x² ⁻ 6. is divided by (x - 2).

It means that if P (x) is divided by (x - 2) and leaves a Remainder, it implies that x - 2 is not a factor of P (x), but if it leaves no remainder, it means x-2 is a factor of P (x).

Therefore, to find the remainder, find the zero of x - 2, and substitutes for the value in P (x) to know the remainder

x - 2 = 0

x = 2

Now put this in P (x)

P (x) = 2 (2) ⁴ - (2) ³ + 2 (2) ² - 6

= 2 (16) - 8 + 2 (4) - 6

= 32 - 8 + 8 - 6

=26

Therefore the remainder when P (x) is divided by x - 2

=26

Note: Since the division of P (x) by x - 2 leaves a remainder, it means that

x - 2 ≠ a factor of P (x)