Hi, HCF is the ploynomial with the highest degree that occurs in both. You could also have divided the polynomials, and sort of used the Euclidean algorithm and keep going until remainder is zero, like you would with two integers. Thanks for doing the question. Reason I submitted question was I had not seen HCF of polynomials before, only using algorithm for integers before.
Euclidean algorithm always works. I was baffled by it and gave it much thought few years after learning it. Let us consider the division of numbers/polynomials etc with remainder A=Q*B+R where R
For the current problem at step 1 A=2x^2+3x^2+3x+1 B=x^3-x^2-x-2 R1=A-2B=5(x^2+X+1) R2=B-R1*(X/5)=-2x^2-2x-2+2/5R1=0 Well the largest common divisor should be x^2+X+1
Hi, HCF is the ploynomial with the highest degree that occurs in both. You could also have divided the polynomials, and sort of used the Euclidean algorithm and keep going until remainder is zero, like you would with two integers. Thanks for doing the question. Reason I submitted question was I had not seen HCF of polynomials before, only using algorithm for integers before.
Euclidean algorithm always works. I was baffled by it and gave it much thought few years after learning it.
Let us consider the division of numbers/polynomials etc with remainder
A=Q*B+R where R
For the current problem at step 1
A=2x^2+3x^2+3x+1
B=x^3-x^2-x-2
R1=A-2B=5(x^2+X+1)
R2=B-R1*(X/5)=-2x^2-2x-2+2/5R1=0
Well the largest common divisor should be x^2+X+1
@@dan-florinchereches4892 Good old Euclidean algorithm, works with integers or polynomials!!