Question

Find HCF 2x^5-4x^4-6x and x^5+x^4-3x^3-3x^2

Answer 1

HCF =
`(x + 1)`

Explanation:

A common factor is a factor that is shared by two or more numbers (or, in this case, polynomials). The highest common factor (HCF) is found by finding all common factors of the two expressions and selecting the largest one.

Find HCF of
`2x^5-4x^4-6x \ \ \textsf{and} \ \ x^5+x^4-3x^3-3x^2`

Factor
`2x^5-4x^4-6x`

Factor out common term:
`2x(x^4-2x^3-3)`

Factor
`x^4-2x^3-3`:
`2x(x+1)(x^3-3x^2+3x-3)`

Factor
`x^5+x^4-3x^3-3x^2`

Factor out common term:
`x^2(x^3+x^2-3x-3)`

Factor
`x^3+x^2-3x-3`:
`x^2(x+1)(x+√(3) )(x-√(3) )`

Therefore, from inspection the HCF =
`(x + 1)`