Question

please give my answer ​

Answer 1

Answer:

Here is your answer mate...

Explanation:

(i) By arranging the two polynomials in the descending order of powers of x we get,

4a4 – 20a3 + 40a2 – 32a and 2a4 – 8a3 + 14a2 – 12a

(ii) By taking out the common factors from the terms of the expressions we get,

4a4 – 20a3 + 40a2 – 32a

= 4a(a3 – 5a2 + 10a – 8) 2a4 – 8a3 + 14a2– 12a

= 2a(a3 – 4a2 + 7a – 6)

At the time of writing the final result the H.C.F. of 4a and 2a i.e. 2a is to be multiplied with the divisor of the last step.

(iii)

H.C.F. of Polynomials by Long Division Method

Therefore, the H.C.F. of 4a4 + 40a2 – 20a3 – 32a and 2a4 – 12a – 8a3 + 14a2 is 2a(a – 2)

2. Find the H.C.F. of 6m3 – 17m2 – 5m + 6, 6m3 – 5m2 – 3m + 2 and 3m3 – 7m2 + 4 by using long division method.

Answer 2

ans.2 In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common divisor of two integers.

ans.3    Definition of factorization. : the operation of resolving a quantity into factors also : a product obtained by factorization.