CBSE Class 10 Maths solutions Polynomials Ex 2.3 | Step-by-step Division Algorithm for Polynomials

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http://www.learncbse.in/polynomials-cbse-class-10-maths-chapter-2-extra-questions/

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00:02 Q1. Divide the polynomial p ( x ) by the polynomial g ( x) and find the quotient and remainder in each of the following :

00:20 (i) Divide the polynomial p(x) = x^3 – 3x^2 + 5 x – 3 by the polynomial g(x) = x^2– 2.

00:34 Division Algorithm for polynomials

01:00 Step 1 To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor .Then carry out the division process. What remains is our new dividend

01:14 Step 2 : Now, to obtain the second term of the quotient, divide the highest degree term of the new dividend by the highest degree term of the divisor.Again carry out the division process.

01:49 Step 3 : Carry the division process untill the degree of the remainder is less than the degree of the divisor

03:46 (ii)Divide the polynomial p(x) = x^4 – 3x^2 + 4x + 5 by the polynomial g(x)= x^2+1-x

04:12 Arrange the terms in Standard Form.

08:40 (iii)Divide the polynomial p(x)= x^4 –5x +6 by the polynomial g(x)=2–x^2

11:50 Q2. Check whether the first polynomial is a factor of the second polynomial by dividing the

second polynomial by the first polynomial:

12:23 (i) Is the polynomial t^2 – 3 is a factor of the polynomial 2t^4 + 3 t^3 – 2 t^2 – 9 t – 12.

12:26 Procedure for Division Algorithm for polynomials

12:53 Step 1 To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor .Then carry out the division process. What remains is our new dividend

13:23 Step 2 : Now, to obtain the second term of the quotient, divide the highest degree term of the new dividend by the highest degree term of the divisor.Again carry out the division process.

13:35 Step 3 : Carry the division process untill the degree of the remainder is less than the degree of the divisor

16:38 (ii) Is the polynomial x^2 + 3 x + 1 is a factor of the polynomial 3 x^4 + 5 x^3 – 7 x^2 + 2 x + 2

21:37 (iii) Is the polynomial x^3 – 3 x + 1 is a factor of the polynomial x^5 – 4 x^3 + x^2 + 3 x + 1x

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