without actual division prove that 2 x ^ 4 - 5 x cube + 2 x square minus x + 2 is divisible by x square minus 3 X + 2
Answers
Answered by
33
x^2- 3x+2
=> x^2- 2x- 1x+2
=> x(x-2) -1(x-2)
=> (x-1) (x-2)
x-1=0
x=1
x-2=0
x=2
p(x)= 2x^4-5x^3+2x^2-x+2
p(1)=2(1)^4 - 5(1)^3+2(1)^2-1+2
= 2-5+2-1+2
=6-6
=0
p(2)=2(2)^4-5(2)^3+2(2)^2-2+2
= 32-40+8
= 40-40
= 0
so, (x-1) and (x-2) are the factors of the polynomial 2x^4-5x^3+2x^2-x+2.
Hence, 2x^4-5x^3+2x^2-x+2 is divisible by x^2-3x+2
=> x^2- 2x- 1x+2
=> x(x-2) -1(x-2)
=> (x-1) (x-2)
x-1=0
x=1
x-2=0
x=2
p(x)= 2x^4-5x^3+2x^2-x+2
p(1)=2(1)^4 - 5(1)^3+2(1)^2-1+2
= 2-5+2-1+2
=6-6
=0
p(2)=2(2)^4-5(2)^3+2(2)^2-2+2
= 32-40+8
= 40-40
= 0
so, (x-1) and (x-2) are the factors of the polynomial 2x^4-5x^3+2x^2-x+2.
Hence, 2x^4-5x^3+2x^2-x+2 is divisible by x^2-3x+2
Answered by
2
Answer:
Step-by-step explanation:
First find the value of x from 2nd polynomial.
Then substitute f(x) from the first polynomial.
If the remainder comes as 0 then it is divisible.
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