Question

without actual division show that the polynomial 2x square - 5 x cube + 2 x square minus x + 2 is exactly divisible by x square - 3 x + 2

Answer 1

нєℓℓσ мαтє!

p( x ) = 2x⁴ - 5x³ + 2x² - x + 2

Now, factor x² - 3x + 2 = 0
x² - 2x - x + 2 = 0
x ( x - 2 ) - 1 ( x - 2 ) = 0
( x - 1 )( x - 2 ) = 0

So, x = 1 or 2

p( 1 ) = 2( 1 )⁴ - 5( 1 )³ + 2( 1 )² - 1 + 2
0 = 2 - 5 + 2 - 1 + 2
0 = 0

p( 2 ) = 2( 2 )⁴ - 5( 2 )³ + 2( 2 )² - 2 + 2
0 = 32 - 40 + 8 - 2 + 2
0 = 0

нєи¢є, ωιтнσυт α¢тυαℓℓ ∂ινιѕισи ωє ρяσνє∂ тнαт gινєи ρσℓуиσмιαℓ ιѕ ∂ινιѕιвℓє ву ιтѕ ∂ινιѕσя.

нσρє ιт нєℓρѕ☺️!✌️