University:
Texas A&M University
Course:
MATH 102 | Algebra
Academic year:

2021
Views:

202

Pages:

3
Author:

5prinzg1s

MATHS POLYNOMIALS DEGREE OF POLYNOMIAL DEGREE OF POLYNOMIAL The greatest power (exponent) of the terms of a polynomial is called degree of the polynomial. For example : (a) In polynomial 5x2 – 8x7 + 3x : (i) The power of term 5x2 = 2 (ii) The power of term –8x7 = 7 (iii) The power of 3x = 1 Since, the greatest power is 7, therefore degree of the polynomial 5x2 – 8x7 + 3x is 7 (b) The degree of polynomial : (i) 4y3 – 3y + 8 is 3 (ii) 7p + 2 is 1(p = p1) (iii) 2m – 7m8 + m13 is 13 and so on. Degree of a Polynomial in One Variable : In case of a polynomial in one variable, the highest power of the variable is called the degree of the polynomial. For example: the degree of 9x3 + 8x2 + x – 7 is 3. Degree of a Polynomial in Two or More Variables : In case of polynomials in more than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is called the degree of the polynomial. 1 MATHS For example: the degree of 5x3 + 6x2y2 + 12y3 is 2 + 2 = 4. Because the power of the variables in first and third terms is 3 but the sum of power of variables in second term is 4 and 4 > 3. Hence the degree is 4. Additive Inverse of a Polynomial : A polynomial Q is the additive inverse of a polynomial P if the sum of Q and P is zero, e.g. 3x2 – 5x + 7 is the additive inverse of –3x2 + 5x – 7. The additive inverse of a polynomial is obtained by reversing the sign of each of the coefficients of the polynomial. Zero Degree Polynomial : Any non-zero number is regarded as a polynomial of degree zero or zero degree polynomial. For example, f(x) = a, where a0 is a zero degree polynomial, since we can write f(x) = a as f(x) = ax0. Constant Polynomial : A polynomial of degree zero is called a constant polynomial. For example, f(x) = 7. Ex.1 Sol. Find which of the following algebraic expression is a polynomial. 1 x (i) 3x2 – 5x (ii) x + (iii) y – 8 (iv) z5 – 3 z + 8 (i) 3x2 – 5x = 3x2 – 5x1 It is a polynomial. 2 MATHS (ii) x + 1 = x1 + x–1 x It is not a polynomial. (iii) y – 8 = y1/2 – 8 Since, the power of the first term ( y ) is 1 , which is not a whole number. 2 (iv) z5 – 3 z + 8 = z5 – z1/3 + 8 Since, the exponent of the second term is 1/3, which in not a whole number. Therefore, the given expression is not a polynomial. 3