Question

Please take Madam Phote of question good way
[
begin{array}{l}
x^{2}-3 x+2 text { divides }
p(x)=2 x^{4}-5 x^{3}+2 x^{2}-x+2
end{array}
]
means rasats of ( u^{2}-3 x+2=0 ) is abo the revets of ( mathrm{P}(mathrm{N}) )
[
begin{array}{l}
text { 80240 } begin{array}{c}
x^{2}-3 x+2=0
(x-2)(x-1)=0
x=1,2
end{array}
begin{aligned}
P(1)=& 2-5+2-1+2
=& 6-6
=& 6
=& 2 times 2^{4}-5 x_{2}^{3}+2 x_{2}^{2}-2+2
=& 32=40+8-2+2
=& 42-42
=& 0
end{aligned}
end{array}
]
thence poved, pow is is an

# 19. Without actual division, prove that 2x–5x+ 2x -x+2 is divisible by x2-3x+2.

Solution