Question

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

Answer 1

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)