What would be the gcf for these polynomials equations? (1) 2x3 - 8x2 - 9x + 36 (2) 6x4 -10x³ + 3x².PLEASE HELP!!!
To find the greatest common factor (GCF) for the given polynomial equations, we need to factor each polynomial and find their common factors.
Let's start with the first polynomial equation: 2x^3 - 8x^2 - 9x + 36.
Step 1: Group the terms if possible.
2x^3 - 8x^2 - 9x + 36 = (2x^3 - 8x^2) + (-9x + 36).
Step 2: Factor out the common terms from each group.
The common factor in the first group is 2x^2, which gives us: 2x^2(x - 4).
The common factor in the second group is -9, which gives us: -9(x - 4).
Step 3: Find the common factors between the two groups.
Both groups have the factor (x - 4) in common.
Therefore, the GCF of the first polynomial is (x - 4).
Now let's move to the second polynomial equation: 6x^4 - 10x^3 + 3x^2.
Step 1: Group the terms if possible.
6x^4 - 10x^3 + 3x^2 = (6x^4 - 10x^3) + (3x^2).
Step 2: Factor out the common terms from each group.
The common factor in the first group is 2x^3, which gives us: 2x^3(3x - 5).
The second group doesn't have any common factors.
Therefore, the GCF of the second polynomial is 2x^3.
In conclusion, the GCF for the given polynomial equations is:
(1) GCF = x - 4
(2) GCF = 2x^3