Problema Solution
How do we find the greatest common factor of a polynomial? Demonstrate the process with an example showing your work. When finding the greatest common factor of a polynomial, can the factor ever be larger than the smallest coefficient? Can it ever be smaller than the smallest coefficient?
Answer provided by our tutors
You find the GCF of a polynomial by first finding the GCF of the numbers, then finding the GCF of the variables (always take the lowest exponent).
For example, find the GCF of 15x^3 - 20x^2 +80x
The GCF of 15, 20, and 80 is 5 since 5 is the highest number that divides into each evenly
The GCF of x^3, x^2, and x is x since x divides into each evenly
So the GCF is 5x
The factored expression is 5x(3x^2-4x+16)
The factor cannot be larger than the smallest coefficient; however it can be the smallest coefficient. If I had used 5 instead of 15 in the expression above, 5 would be the GCF.