Question

Without actual division prove that (x²-x-2) divides 2x + x³ - 5x²​

Answer 1

Step-by-step explanation:

∵P(x)=2x

4

−5x

3

+2x

2

−x+2

andx

2

−3x+2=(x−1)(x−2)

letx

2

−3x+2isthefactorofP(x)

then,x

2

−3x+2=0

⇒(x−1)(x−2)=0

⇒x=1and2

forx=1

P(1)=0

andforx=2

P(2)=0

∵P(1)=P(2)=0

∴P(x)isdivisiblebyx

2

−3x+2