1. The GCD of two polynomials is `x+3` and their LCM is `x^3-7x+6`. If one of the polynomials is `x^2+2x-3`, then the other polynomial
Solution:
We know that `"GCD "*" LCM" = "Poly1 " * "Poly2"`
`:."Poly2 = "("GCD "*" LCM")/("Poly1")`
`=((x+3)(x^3-7x+6))/(x^2+2x-3)`
`=((x+3)^2(x-1)(x-2))/((x-1)(x+3))`
`=(x+3)(x-2)`
`=x^2+x-6`
2. The GCD of two polynomials is `x+1` and their LCM is `x^6-1`. If one of the polynomials is `x^3+1`, then the other polynomial
Solution:
We know that `"GCD "*" LCM" = "Poly1 " * "Poly2"`
`:."Poly2 = "("GCD "*" LCM")/("Poly1")`
`=((x+1)(x^6-1))/(x^3+1)`
`=((x+1)^2(x-1)(x^2+x+1)(x^2-x+1))/((x+1)(x^2-x+1))`
`=(x+1)(x-1)(x^2+x+1)`
`=x^4+x^3-x-1`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
