Look at this trinomial
32a^4 + 18a^3 - 12a
Write the polynomial as the product of the GCF of all its terms and a polynomial
PLEase explain thanks
To express the given trinomial 32a^4 + 18a^3 - 12a as the product of the greatest common factor (GCF) and a polynomial, we need to find the GCF of all the terms.
Step 1: Identify the factors of each term.
The factors of 32a^4 are 1, 2, 4, 8, 16, 32, a, a^2, a^3, and a^4.
The factors of 18a^3 are 1, 2, 3, 6, 9, 18, a, a^2, and a^3.
The factors of 12a are 1, 2, 3, 4, 6, 12, a.
Step 2: Determine the common factors.
The common factors of all three terms are 1, 2, and a.
Step 3: Find the GCF.
The GCF is the product of all the common factors.
GCF = 1 * 2 * a = 2a.
Step 4: Divide each term by the GCF.
(32a^4 / 2a) + (18a^3 / 2a) + (-12a / 2a) = 16a^3 + 9a^2 - 6.
Therefore, the trinomial 32a^4 + 18a^3 - 12a can be written as the product of the GCF (2a) and the polynomial (16a^3 + 9a^2 - 6).