What is the first step in factoring polynomials?

What is the first step in factoring polynomials?

• A. Factor by grouping.
• B. Look for a common square.
• C. Split linear factors.
• D. Always factor out the greatest common factor first.

Answer: (D)

The first move when factoring a polynomial is to factor out the greatest common factor from all terms. Pulling out this common factor simplifies the expression and often reveals further factoring opportunities that weren’t visible before. To do this, find the largest numeric factor and the lowest power of any common variables present in every term, then rewrite the polynomial as the GCF multiplied by the remaining factor. For example, 8x^3 + 12x^2 becomes 4x^2(2x + 3). After removing the GCF, you then check the remaining factor to see what other factoring method applies. Grouping, looking for a square, or splitting linear factors are techniques used later or in specific forms, but they don’t represent the first step in general factoring.

The first move when factoring a polynomial is to factor out the greatest common factor from all terms. Pulling out this common factor simplifies the expression and often reveals further factoring opportunities that weren’t visible before. To do this, find the largest numeric factor and the lowest power of any common variables present in every term, then rewrite the polynomial as the GCF multiplied by the remaining factor. For example, 8x^3 + 12x^2 becomes 4x^2(2x + 3). After removing the GCF, you then check the remaining factor to see what other factoring method applies. Grouping, looking for a square, or splitting linear factors are techniques used later or in specific forms, but they don’t represent the first step in general factoring.