Which step is a standard first step when solving a quadratic equation by factoring?

Which step is a standard first step when solving a quadratic equation by factoring?

• A. Set the equation equal to zero
• B. Take the square root of each side
• C. Graph the function
• D. Divide both sides by a

Answer: (A)

The key idea is to get the equation in a form that can be factored: you want all terms on one side so the expression equals zero. When you have a quadratic written as ax^2 + bx + c = 0, you can look for two numbers that multiply to ac and add to b, or factor the left side directly into a product of binomials. Once it’s factored, you apply the zero product property by setting each factor equal to zero to find the solutions. Taking the square root is only appropriate if you’ve already isolated a perfect square on one side, like x^2 = k, which isn’t the general first step for factoring a quadratic. Graphing can show where the roots lie but doesn’t give the exact algebraic factorization. Dividing by a is not a universal first step for factoring and can be inappropriate if a is zero or if you still need the standard form to factor.

The key idea is to get the equation in a form that can be factored: you want all terms on one side so the expression equals zero. When you have a quadratic written as ax^2 + bx + c = 0, you can look for two numbers that multiply to ac and add to b, or factor the left side directly into a product of binomials. Once it’s factored, you apply the zero product property by setting each factor equal to zero to find the solutions.

Taking the square root is only appropriate if you’ve already isolated a perfect square on one side, like x^2 = k, which isn’t the general first step for factoring a quadratic. Graphing can show where the roots lie but doesn’t give the exact algebraic factorization. Dividing by a is not a universal first step for factoring and can be inappropriate if a is zero or if you still need the standard form to factor.