Question

without actual division prove that f(x) = 2x⁴ -6x³+3x²+3x-2 exactly divisible by x² - 3x +2​

Answer 1

Answer:

Step-by-step explanation:

let p(X)= 2x⁴-5x³+2x²-x+2

g(X) x²-3x+2

by splitting middle term

x²-2x-x+3

x(x-2)+1(x-2)

(x-1)(x-2)

x-1=0. x-2=0

X=1. X=2

using remainder theorem ,put any value of X in p(X)

p(1)= 2×(1)⁴-5(1)³+2(1)²-1+2

= 2×1-5×1+2×1-1+2

=2-5+2-1+2

= 0

rem =0

therefore,p(X) is exactly divisible by X²-3x+2