Unit 1.2.1: Polynomial
Exercise 1.2.1
1. (a) Define polynomial of one variable.
Solution:
A polynomial in one variable is any expression of the type
where is non-negative integer and are real numbers, called coefficients. is called the leading term of the polynomial. is degree of the polynomial.
(b) If and represent polynomial, quotient, divisor and remainder respectively. Write the relation among them.
Solution:
We know, Polynomial = Divisor x Quotient + Remainder
2. Divide using long division method and find quotient and remainder in each of the following:
(a)
Solution:
Quotient and remainder
(b)
Solution:
Quotient and Remainder
(c)
Solution:
Quotient and Remainder
(d)
Solution:
Quotient Remainder
3. Divide using long division method and find quotient and remainder.
(a)
Solution:
Quotient and Remainder
(b)
Solution:
Quotient and Remainder
(c)
Solution:
Quotient and Remainder
(d)
Solution:
Quotient and Remainder
4. For the function use long division to determine whether each of the following is a factor of or not.
(a)
Solution:
Here, remainder is 0. So is a factor of
(b)
Solution:
Since, remainder is 0, is a factor of
(c)
Solution:
As remainder , is not factor of
(d)
Solution:
As remainder , is not a factor of .
(e)
Solution:
As remainder , is a factor of
5. For the polynomial and divisor use long division to find the quotient and the remainder when is divided by Express in the form of Write your finding.
Solution:
Here,
Now,
Hence, Quotient
Remainder
We know,
Quotient and remainder
(b)
Solution:
Quotient and Remainder
(c)
Solution:
Quotient and Remainder
(d)
Solution:
Quotient Remainder
3. Divide using long division method and find quotient and remainder.
(a)
Solution:
Quotient and Remainder
(b)
Solution:
Quotient and Remainder
(c)
Solution:
Quotient and Remainder
(d)
Solution:
Quotient and Remainder
4. For the function use long division to determine whether each of the following is a factor of or not.
(a)
Solution:
Here, remainder is 0. So is a factor of
(b)
Solution:
Since, remainder is 0, is a factor of
(c)
Solution:
As remainder , is not factor of
(d)
Solution:
As remainder , is not a factor of .
(e)
Solution:
As remainder , is a factor of
5. For the polynomial and divisor use long division to find the quotient and the remainder when is divided by Express in the form of Write your finding.
Solution:
Here,
Now,
Hence, Quotient
Remainder
We know,