Learn how to factor a quadratic when a is not one to solve the equation

The video tutorial explains how to solve quadratic equations by factoring, especially when the leading coefficient is not one. It covers setting the equation to zero, factoring out the greatest common factor, and using the zero product property. The instructor highlights common mistakes and demonstrates the correct method for finding factors and grouping terms.

What is the first step in solving a quadratic equation by factoring?

• Set the equation equal to zero

• Multiply both sides by a constant

• Add a constant to both sides

• Divide both sides by a variable

Why is it important to factor out the greatest common factor (GCF) in a quadratic equation?

• To make the equation more complex

• To simplify the equation for easier factoring

• To change the equation's roots

• To eliminate the variable

When factoring a quadratic equation, what do the two numbers need to do?

• Multiply to give the constant term

• Add to give the coefficient of the linear term

• Add to give the leading coefficient

• Multiply to give the product of the leading coefficient and constant term

What mistake do students commonly make when factoring quadratics with a leading coefficient not equal to 1?

• Ignoring the constant term

• Using incorrect signs for the factors

• Assuming the factors are the same as when the leading coefficient is 1

• Forgetting to set the equation to zero

What is the purpose of breaking apart the middle term in a quadratic equation?

• To change the equation's roots

• To simplify the equation

• To prepare for grouping terms

• To eliminate the constant term

What is the Zero Product Property used for in solving quadratic equations?

• To find the sum of the roots

• To divide the equation by zero

• To set each factor equal to zero

• To multiply the factors

In the final step of factoring by grouping, what should you do after factoring out the common element?

• Add the factors together

• Multiply the factors

• Set each factor equal to zero

• Divide the factors by a constant