What method is used to check your work when factoring?

What method is used to check your work when factoring?

• A. Apply the distributive property to reverse the factoring.
• B. Check by substituting a value for the variable and verifying equality.
• C. Use the FOIL method to expand the factors back to the original expression.
• D. Use the quadratic formula on the original factors.

Answer: (C)

Verifying factoring by expanding the factors to recover the original polynomial is the best way to check. When you factor a polynomial, you’re expressing it as a product of simpler factors, so multiplying those factors back together should yield the exact original expression. Using FOIL—First, Outer, Inner, Last—is the standard method for expanding two binomials, and it lets you confirm the match precisely. For example, if you factor a quadratic into (x+2)(x+3), expanding gives x^2 + 3x + 2x + 6, which simplifies back to x^2 + 5x + 6, proving the factorization is correct. Substituting a single value for the variable only checks one case and doesn’t prove the factorization works for all x. The quadratic formula is for solving equations, not for verifying a factorization.

Verifying factoring by expanding the factors to recover the original polynomial is the best way to check. When you factor a polynomial, you’re expressing it as a product of simpler factors, so multiplying those factors back together should yield the exact original expression. Using FOIL—First, Outer, Inner, Last—is the standard method for expanding two binomials, and it lets you confirm the match precisely. For example, if you factor a quadratic into (x+2)(x+3), expanding gives x^2 + 3x + 2x + 6, which simplifies back to x^2 + 5x + 6, proving the factorization is correct. Substituting a single value for the variable only checks one case and doesn’t prove the factorization works for all x. The quadratic formula is for solving equations, not for verifying a factorization.