Question

without actual division prove that
2x^4-5x^3 +2x^² - x+2 is divided
& by
x^2-3x +2​

Answer 1

Answer:

hhgik

Step-by-step explanation:

hgipuhbbbjkkkhhhkkg hioh

Answer 2

Step-by-step explanation:

Question:- Without actual division prove that

2x^4-5x^3 +2x^2 - x+2 is divisible by x^2-3x +2.

Solution:- x^2 - x 2x + 2 = x^2 - x -2x +2

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

= (x - 1)(x - 2)

Let p(x) = 12x^4-5x^3 +2x^2 - x+2

Now p(1) = 2(2)^4 - 5(1)^3 + 2(1)^2 - 1 + 2

= 2 - 5 + 2 - 1 + 2

= 6 - 6

= 0

Therefore, (x - 1) divides p(x)

and

p(2) = 2(2)^4 - 5(2)^3 + 2(2)^2 -2 + 2

= 32 - 40 + 8 - 2 + 2

= 42 - 42

= 0

Therefore, (x - 2) divides p(x)

So, (x - 1)(x - 2) = x^2 - 3x + 2 divides 12x^4-5x^3 +2x^2 - x+2.

:)