Question

1 DOT 4) Luu
lons
23. Without actual división, prove that 2x4 – 5x + 2x2 - x +2 is divisible by
x²-3x+2.
2.4 .3 122
that there
.without actual division prove that 2 x power 4 minus 5 x power 3 + 2 x power 2 - X + 2 is divisible by divisible by 2 x square - 3 x + 2 ​

Answer 1

Answer:

Step-by-step explanation

f(x)=x4-5x3+2x2-x+2

X2-3x+2

=x2-2x-x+2

=X(x-2)-(x-2)

=(x-2(x-1)

X=1,2

Putting X=1in f(X)

2*1-5+2-1+2

=2-5+2-1+2=0

and

f(2)=2*16-5*8-2*4-2+2=0

Hence x-1 and x-2 are factor of f(X)

Or (x-1)(x-2) are factor of f(X)

So f(X) is divisible by x2-3x+2