Unit 1.2.3(A): Some theorems on polynomials
- Author:
- AMBIK BARAL
1. (a) State remainder theorem.
Solution:
If a polynomial is divided by then the remainder is .
1. (b) If divides what is the remainder ?
Solution:
Here, zero of polynomial .
Remainder
2. Use remainder theorem and find the remainder in each of the following:
(a)
Solution:
Let,
Zero of polynomial is 2.
(b)
Solution:
Let,
Zero of polynomial is
(c)
Solution:
Let,
Zero of polynomial is
(d)
Solution:
Solution:
Let,
Zero of polynomial is
(e)
Solution:
Let,
Zero of polynomial is
(f)
Solution:
Let,
Zero of polynomial is
(g)
Solution:
Let,
Zero of polynomial is
3. (a) If is divided by , the remainder is 4, find the value of , using remainder theorem.
Solution:
Let,
Zero of is 2.
3. (b) If is divided by , the remainder is 6, find the value of , using remainder theorem.
Solution:
Let,
Zero of is 5.
3. (c) If and , both are divided by , remainder is same, find the value of .
Solution:
Let,
And
Zero of is 1.
By question the remainder is same,
so,
3. (d) If divides the polynomials and to get the same remainder, find the value of .
Solution:
Let,
And
Zero of is 2.
By question the remainder is same,
so,
4. Take a polynomial function. Take any three linear divisors in the form of . Use remainder theorem and find the remainder.
Solution: