 ×     #### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```
If a polynomial P(x) is divided by x-a, x-b, x-c, we get a,b,c as remainders respectively (x€R). Then what will be the remainder when P(x) is divided by (x-a)(x-b)(x-c)?

```
4 years ago Harsh Patodia
IIT Roorkee
907 Points
```							Using Remiander theoremf(a) is the remainder when f(x) is divided by x-awhen f(x) is divided by q(x) the remainder will be having degree less than q(x) so when P(x) is divided by (x-a),(x-b),(x-c) the remainders are P(a),P(b) and P(c) respectivelytherefore P(x)=(x-a)(x-b)(x-c)g(x) + (px^2+qx+r) where (px^2+qx+r)is remainder g(x) is the quotientP(a)=pa^2+qa+r=a --- (I)P(b)=pb^2+qb+r=b----(II)P(c)=pc^2+qc+r=c-----(III)Closely observing u can q=1 p and r =0So remiander will be xand Secondly you could have also solved equations by using II-I and III-I.
```
4 years ago
```							Note that P(a) =a, P(b) = b, and P(c) = c. Hence if we consider the polynomial Q(x) = P(x) – x, we see that Q(a) = Q(b) = Q(c) = 0. By Factor theorem we conclude (x-a)(x-b)(x-c) is a factor of Q(x). i.e. Q(x) = (x-a)(x-b)(x-c) R(x) for some polynomial R(x). so that P(x) – x = (x-a)(x-b)(x-c) R(x) or P(x) = (x-a)(x-b)(x-c) R(x)+x From the above eqn is evident that when P(x) is divided by (x-a)(x-b)(x-c), the remainder is x
```
4 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions