Polynomial question! (1 Viewer)

[YBK]

could anyone please help me out with this one:

P(x) has remainder x - 2 when divided by x^2 - 1
Find the remainder when P(x) is divided by x + 1

Well, I did:

P(x)/x^2+1= x - 2

then i got P(x) = (x^2 + 1) (x - 2)
and replaced x by -1 giving a remainder of 0

is this correct?

Thanks

 

[robbo_145]

could anyone please help me out with this one:

P(x) has remainder x - 2 when divided by x^2 - 1
Find the remainder when P(x) is divided by x + 1

Well, I did:

P(x)/x^2+1= x - 2

then i got P(x) = (x^2 + 1) (x - 2)
and replaced x by -1 giving a remainder of 0

is this correct?

Thanks

P(x) = (x²-1)Q(x) + x - 2 where Q(x) is some other polynomial
P(-1) = 0 - 1 - 2
∴ remainder = -3

 

[YBK]

P(x) = (x²-1)Q(x) + x - 2 where Q(x) is some other polynomial
P(-1) = 0 - 1 - 2
∴ remainder = -3

Thank you!

I knew the way I did it was wrong.... i could just feel it

 

[robbo_145]

haha thats alright, i see your doing your HSC next year so its okay

P(x)/x^2+1= x - 2

a few lines before my first to explain it a bit better

P(x)/(x²+1) = Q(x) + (x - 2)/(x²+1)
hence
P(x) = (x²+1)Q(x) + (x - 2)

 

[YBK]

haha thats alright, i see your doing your HSC next year so its okay



a few lines before my first to explain it a bit better

P(x)/(x²+1) = Q(x) + (x - 2)/(x²+1)
hence
P(x) = (x²+1)Q(x) + (x - 2)

yeah, that makes a lot of sense

Division transformation comes in handy... lol P(x) = D(x) . Q(x) + R(x)