check all of the possible first steps in factoring a polynomial with four terms. factor out a gcf factor the…

check all of the possible first steps in factoring a polynomial with four terms. factor out a gcf factor the difference of cubes factor a sum of cubes factor a difference of squares factor a perfect - square trinomial factor by grouping done

check all of the possible first steps in factoring a polynomial with four terms. factor out a gcf factor the difference of cubes factor a sum of cubes factor a difference of squares factor a perfect - square trinomial factor by grouping done

Answer

Answer:

  • factor out a GCF
  • factor by grouping

Explanation:

Step1: Analyze GCF

When factoring any polynomial, checking for a greatest - common factor (GCF) among all terms is a valid first step. For a four - term polynomial, this simplifies the expression.

Step2: Analyze grouping

Grouping is a common first step for four - term polynomials. We group the terms in pairs and then factor out the GCF from each pair.

Step3: Analyze other options

The difference of cubes ($a^{3}-b^{3}=(a - b)(a^{2}+ab + b^{2})$), sum of cubes ($a^{3}+b^{3}=(a + b)(a^{2}-ab + b^{2})$), difference of squares ($a^{2}-b^{2}=(a + b)(a - b)$), and perfect - square trinomials ($a^{2}+2ab + b^{2}=(a + b)^{2}$ or $a^{2}-2ab + b^{2}=(a - b)^{2}$) are not applicable as first steps for a general four - term polynomial. They are for specific forms of polynomials with 3 or 2 terms in certain patterns.