Polynomials Question---need Help!!! (1 Viewer)

[screwed8899]

When a polynomial P(x) is divided by x+3 the remainder is 8 and when divided by x-2 the remainder is 3. Find the remainder when P(x) is divided by (x-2)(x+3).

I got no idea what so ever...any help would be apprieciated!!

 

[haboozin]

could it be 24??
or 11


but dividing by that could give you a remainder in the form of ax + b , but then again a could be 0?

 

[screwed8899]

the answer was -x+5

i just got no idea on how 2 get that

 

[香港!]

When a polynomial P(x) is divided by x+3 the remainder is 8 and when divided by x-2 the remainder is 3. Find the remainder when P(x) is divided by (x-2)(x+3).

I got no idea what so ever...any help would be apprieciated!!

let cx+d be the remainder when the polynomial p(x) is divided by (x-2)(x+3)
Now we have:
p(x)=(x-2)(x+3)q(x)+(cx+d)

"When a polynomial P(x) is divided by x+3 the remainder is 8"
.: p(-3)=8
-3c+d=8
d=8+3c

"when divided by x-2 the remainder is 3"
.: p(2)=3
2c+d=3
2c+8+3c=3
5c=-5
.: c=-1
d=8-3=5

.: the remainder when P(x) is divided by (x-2)(x+3) is:
-x+5

 

[screwed8899]

Thanx alot!!!

 

[Trebla]

When a polynomial P(x) is divided by x+3 the remainder is 8 and when divided by x-2 the remainder is 3. Find the remainder when P(x) is divided by (x-2)(x+3).

I got no idea what so ever...any help would be apprieciated!!

__P(x)__ : remainder is 8
(x + 3)

.(-3) = 8 <=== (A)

__P(x)__ : remainder is 3
(x - 2)

.: P(2) = 3 <=== (B)

____P(x)____ : remainder is (ax +b)
(x - 2)(x + 3)

Now: writing in the form: P(x) = A(x).Q(x) + R(x)
.: P(x) = (x - 2)(x + 3).Q(x) + (ax + b)

Subs x = 2
P(2) = 2a + b
But P(2) = 3 [from (B)]

.: 2a + b = 3 --------- (1)

Subs x = -3
P(-3) = -3a + b
But P(-3) = 8 [from (A)]

.: -3a + b = 8 -------(2)

(2) - (1):
-5a = 5
.: a = -1

Subs a = 5 into (1)
2 x -1 + b = 3
.: b = 5

.: since a = -1, b = 5 and remainder = (ax + b)
.: remainder = -x + 5

 

[haboozin]

oh cool, easy as ... never seen a question like this...