Question

without actual division prove that 2x⁴ -5x³+2x²-x+2 is divisible by x²-3x+2​

Answer 1

Step-by-step explanation:

to prove that 2x⁴ -5x³+2x²-x+2 is divisible by x²-3x+2

x² -3x+2 should be equal to zero

then

=>x²-3x+2 =0

=>x²-2x-x+2 =0

=>x(x-2)-1(x-2)=0

=>(x-2)(x-1)=0

x=1 or x=2

putting

x=2 in 2x⁴ -5x³+2x²-x+2

=2(2)⁴- 5(2)³+2(2)²-2+2

=32-40+8

=0

and x=1 in 2x⁴ -5x³+2x²-x+2

=2(1)⁴-5(1)³+2(1)²-1+2

=2-5+2-1+2

=0