What would be the gcf for these polynomials equations? (1) 2x3 - 8x2 - 9x + 36 (2) 6x4 -10x³ + 3x².PLEASE HELP!!!
(1) GCF= 1
(2) GCF= x^2
I'm pretty sure for the 2nd problem it's x^2 but I don't know about 1 x;
find the greatest common factor of a polynomial? show me how you figure out the answers please!!!! greatly appericate it<3
First, there are no equations. See any "=" signs? You just have two polynomials.
You cannot have a GCF for each polynomial. There is a GCF for the two polynomials. The "common" means shared by two or more things.
The first 2x^3 - 8x^2 - 9x + 36
= (x-4)(2x^2 - 9)
The second 6x^4 -10x^3 + 3x^2
= x^2 (6x^2 - 10x + 3)
There is no factor common to both polynomials, so the GCF = 1
To find the greatest common factor (GCF) for the given polynomial equations, we need to factorize each polynomial and identify their common factors.
First, let's find the GCF for the polynomial equation (1): 2x^3 - 8x^2 - 9x + 36.
1. Start by looking for common factors in the coefficients of the polynomial (the numbers without x).
The coefficients of the polynomial are 2, -8, -9, and 36. The only common factor among these numbers is 1.
2. To find common factors with x, look for the highest power of x that divides all terms of the polynomial.
The highest power of x that divides into each term is x.
Now let's find the factors that can be extracted from the given polynomial:
2x^3 - 8x^2 - 9x + 36 = x(2x^2 - 8x - 9) + 36
Now, let's find the GCF for the polynomial equation (2): 6x^4 - 10x^3 + 3x^2.
1. Start by looking for common factors in the coefficients of the polynomial (the numbers without x).
The coefficients of the polynomial are 6, -10, and 3. The only common factor among these numbers is 1.
2. To find common factors with x, look for the highest power of x that divides all terms of the polynomial.
The highest power of x that divides into each term is x^2.
Now let's find the factors that can be extracted from the given polynomial:
6x^4 - 10x^3 + 3x^2 = x^2(6x^2 - 10x + 3).
Now that we have factored both polynomials, we can compare their factors to find the GCF. In this case, the GCF is x^2:
GCF = x^2
Therefore, the greatest common factor (GCF) for the given polynomial equations is x^2.