Question

without actul division show that p(x)=2x^4-5x^3+2×^2-x+2 is exactly divisible by x^2-3x+2

Answer 1

Hlo friend.. Cutiepie Here..

Here is ur answer :

P(x) = 2x⁴ - 5x³ + 2x² - x + 2

g(x) = x² - 3x + 2

By splitting g(x) , we get

x² - 3x + 2

x² - 2x - 1x + 2

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

( x - 2) ( x - 1)

Putting these value in p(x)

g(x) = x - 2

x = 2

p(2) = 2 (2)⁴ - 5(2)³ + 2(2)² - 2 + 2

= 32 - 40 + 8 - 2 + 2

= 42 - 42

= 0 - - - - - - - - - - eqⁿ (1)


Putting again these value in p(x)

g(x) = x - 1

x = 1

p(1) = 2(1)⁴ - 5(1)³ + 2(1)² - 1 +2

= 2 - 5 + 2 - 1 + 2

= 6 - 6

= 0 - - - - - - - - - - - eqⁿ (2)

From eqⁿ (1) and eqⁿ (2)

2x⁴ - 5x³ + 2x² - x + 2 is exactly divisible by x² - 3x + 2.


HOPE IT HELPS YOU..