# Without actual division, prove that 2x4-5x3-2x2 -x+2 is exactly divisible by x2-3x+2

by splitting x^2-3x+2, we got=

x^2 -2x -1x +2

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

(x-1)(x-2)

so, x=1 & x=2

then, by putting 1 in f(x)

it will be 0

& putting 2 in f(x)

it will again be 0

so it's proved...

• 19

by splitting x^2-3x+2, we get=

x^2 -2x -1x +2

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

(x-1)(x-2)

so, x=1 x=2

then, by putting 1 in f(x)

it will be 0

putting 2 in f(x)

it will again be 0

proved

• 39

by splitting x^2-3x+2, we get=

x^2 -2x -1x +2

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

(x-1)(x-2)

so, x=1 x=2

then, by putting 1 in f(x)

it will be 0

putting 2 in f(x)

it will again be 0

proved

• 6
• -12
Sorrry
• -13
x2- 3x+2=  x2- 2x- 1x+2(splitting middle terms)
= x(x-2) -1(x-2)
= (x-1) (x-2)
x-1=1
x-2=2
p(x)= 2x4-5x3-2x2-x+2
p(1)=2(1)4 - 5(1)​3-2(1)2-1+2
= 2-5-2-1+2
=-4
p(2)=2(2)4-5(2)3-2(2)2-2+2
= 32-40-8
= -16
so, (x-1) and (x-2) are not the factors of the polynomial 2x4-5x3-2x2-x+2.
• 10

by splitting x^2-3x+2, we get=

x^2 -2x -1x +2

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

(x-1)(x-2)

so, x=1 x=2

then, by putting 1 in f(x)

it will be 0

putting 2 in f(x)

it will again be 0

proved

• -3
If you do factorization you will get
x2-3x+2 = x2-2x-1x+2
= x(x-2)-1(x-2)
= (x-1) (x-2)
So now use factor / remainder theorem
p(x)= 2x4-5x3-2x2 -x+2
x-1=0
x=1
p(1) = 2(1)4-5(1)3-2(1)2-(1)+2
= 2 - 5 - 2 -1 + 2
= -4
x-2=0
x = 2
p(2) = 2(2)4-5(2)3-2(2)2-(2)+2
= 32 - 40 - 8
= -16
Therefore, x2-3x+2  is not divisible by 2x4-5x3-2x2 -x+2
• 0

# Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2.[Hint: Factorise x2 – 3x + 2

• 0
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