The greatest common factor of the given polynomial is 6x. This is obtained by factorizing each term in the given polynomial.
What is the greatest common factor of a polynomial?
The largest factor (mostly monomial) that divides the polynomial evenly (all terms in the polynomial) is said to be the greatest common factor.
Finding the greatest common factor:
(i) Factorize each term (monomials) in the given polynomial
(ii) Pick out the common factors from each term
(iii) The product of the common terms will give the greatest common factor.
Calculating the greatest common factor of the polynomial:
Given polynomial is [tex]18x^3-6x[/tex]
There are two monomials in the given polynomial. They are [tex]18x^3[/tex] and 6x.
Factorizing each term:
[tex]18x^3[/tex] = 2 × 3 × 3 × x × x × x
6x = 2 × 3 × x
From this 2, 3, and x are common in both the terms
SO, on multiplying them 2 × 3 × x = 6x
Thus, 6x is the greatest common factor of the given polynomial [tex]18x^3-6x[/tex].
Learn more about the greatest common factor of polynomials here:
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