Use GCF of the the terms to write the Polynomial as the product of two factors.
24y^3 + 6y^2 - 20y
To write the polynomial 24y^3 + 6y^2 - 20y as the product of two factors, we need to find the greatest common factor (GCF) of the terms.
Step 1: Find the GCF of the coefficients (numbers):
The coefficients of the terms (24, 6, -20) are all divisible by 2, so 2 is the GCF of the coefficients.
Step 2: Find the GCF of the variables and their exponents:
The variables in this polynomial are y. By examining the exponents (3, 2, 1), the variable y has a GCF of y^1.
Step 3: Combine the GCFs of the coefficients and variables:
Now, we multiply the GCF of the coefficients (2) with the GCF of the variables (y^1) to get the final GCF as 2y.
Step 4: Divide the polynomial by the GCF:
We divide the original polynomial by the GCF (2y) to get:
(24y^3 + 6y^2 - 20y) / (2y) = 12y^2 + 3y - 10
Therefore, the polynomial 24y^3 + 6y^2 - 20y can be written as the product of two factors: 2y(12y^2 + 3y - 10).