What is the greatest common factor of 8xy5−16x2y3+20x4y4
Answer:
Greatest common factor(GCF) of a polynomial states that the largest polynomial that divides into the polynomials.
Given that: \(8xy^5-16x^2y^3+20x^4y^4\)
First find the GCF of the expression.
The GCF of 8, 16 and 20 is 4.
The GCF of \(x, x^2 and x^4\) is x.
And the
GCF of \(y^5, y^3 and y^4\) is \(y^3\)
Combine these to find the GCF of the polynomial is, \(4xy^3\)
then;
\(8xy^5-16x^2y^3+20x^4y^4\) = \(4xy^3(2y^2-4x+5x^3y)\)
Therefore, the greatest common factor of
\(8xy^5-16x^2y^3+20x^4y^4\) is \(4xy^3\)