Q. 65.0( 1 Vote )

Find out the degree of the polynomials and the leading coefficients of the polynomials given below:

(i)

(ii) 13x3 – x13 – 113

(iii) -77 + 7x2 – x7

(iv) -181 + 0.8y – 8y2 + 115y3 + y8

(v) x7 – 2x3y5 + 3xy4 – 10xy + 10

Answer :

(i) The monomials in the polynomial are called the terms. The highest power of the terms is the degree of the polynomial.


x2 – 2x3 + 5x7x3 – 70x – 8 is a polynomial in x. Here we have 6 monomials x2, – 2x3, + 5x7, –x3, –70x and –8 which are called the terms of the polynomial.


The highest power is 7 so the degree of the polynomial is 7.


(ii) 13x3 – x13 – 113 is a polynomial in x. Here we have 3 monomials and the highest power is 13 so the degree of the polynomial is 13.


(iii) -77 + 7x2 – x7 is a polynomial in x. Here we have 3 monomials and the highest power is 7 so the degree of the polynomial is 7.


(iv) -181 + 0.8y – 8y2 + 115y3 + y8 is a polynomial in x. Here we have 5 monomials and the highest power is 8 so the degree of the polynomial is 8.


(v) x7 – 2x3y5 + 3xy4 – 10xy + 10 is a polynomial in x and y, Here we have 5 monomials.


Term 1: x7 variable x, power of x is 7. Hence the power of the term is 7.


Term 2: – 2x3y5 the variables are x and y; the power of x is 3 and the power of y is 5.


Hence the power of the term – 2x3y5 is 3 + 5 = 8 [Sum of the exponents of variables x and y ].


Term 3: 3xy4 the variables are x and y; the power of x is 1 and the power of y is 4.


Hence the power of the term 3xy4 is 1 + 4 = 5 [Sum of the exponents of variables x and y].


Term 4: – 10xy the variables are x and y; the power of x is 1 and the power of y is 1.


Hence the power of the term -10xy is 1 + 1 = 2 [Sum of the exponents of variables x and y].


Term 5: 10 the constant term and it can be written as 10x0y0. The power of the variables x0y0 is zero. Hence the power of the term 10 is 0.


So the highest power is 8, hence the degree of the polynomial is 8.


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