Find the greatest common factor (GCF) of the polynomial \(12x^3 + 16x^2 + 20x\).
Answer
Step 3: Check your work by distributing the GCF back to each term. \(4x * 3x^2 = 12x^3\), \(4x * 4x = 16x^2\), and \(4x * 5 = 20x\). Since the original polynomial is recovered, \(4x\) is indeed the GCF of the polynomial.
Step 1 ：Step 1: Identify the common factors of the coefficients and the lowest power of \(x\) in each term. The common factor of the coefficients 12, 16, and 20 is 4. The lowest power of \(x\) in each term is \(x\).
Step 2 ：Step 2: Factor out the GCF from each term. \(4x(3x^2 + 4x + 5)\)
Step 3 ：Step 3: Check your work by distributing the GCF back to each term. \(4x * 3x^2 = 12x^3\), \(4x * 4x = 16x^2\), and \(4x * 5 = 20x\). Since the original polynomial is recovered, \(4x\) is indeed the GCF of the polynomial.
