Let's review the different factoring techniques provided in the options:
A. Factoring by grouping: This method involves grouping terms that have a common factor and then factoring out the GCF from each group.
B. Factoring the difference of two cubes: This formula is used to factor expressions of the form [tex]\(A^3 - B^3\)[/tex] into [tex]\((A - B)(A^2 + AB + B^2)\)[/tex].
C. Factoring perfect square trinomials: This technique applies to expressions of the form [tex]\(A^2 + 2AB + B^2\)[/tex] or [tex]\(A^2 - 2AB + B^2\)[/tex], which can be factored into [tex]\((A + B)^2\)[/tex] or [tex]\((A - B)^2\)[/tex], respectively.
D. Factoring out the GCF (Greatest Common Factor): This method involves factoring out the largest common factor from each term of the expression.
E. Factoring the sum of cubes: This involves factoring expressions of the form [tex]\(A^3 + B^3\)[/tex] into [tex]\((A + B)(A^2 - AB + B^2)\)[/tex].
F. Factoring the difference of squares: This technique is used to factor expressions of the form [tex]\(A^2 - B^2\)[/tex] into [tex]\((A + B)(A - B)\)[/tex].
G. Factoring trinomials by trial and error: This is a method where factors of the given trinomial are tried out until the correct one is found.
Given that the correct answer requires matching to a specific factoring technique, understand that each answer fits a particular polynomial structure. Ensure you apply the definitions and formulas accurately to identify which one corresponds to the expression you need to factor.
