Solving Quadratics by Factoring Techniques

What is the primary reason we learn to factor in algebra?

• To perform division

• To simplify expressions

• To graph functions

• To solve quadratic equations

What does the zero product property state about a product that equals zero?

• The product of any number and zero is one

• None of the factors can be zero

• The factors must be equal

• At least one of the factors must be zero

How do you solve a quadratic equation using the zero product property?

• Set each factor equal to zero and solve

• Graph the equation

• Multiply each factor by zero

• Combine like terms

What must be true about the quadratic equation before you can apply the zero product property?

• It must be factorable into two binomials

• It must contain no linear term

• It must be in standard form with the right side equal to zero

• It must be set to equal one

What is the result of factoring the quadratic expression x^2 + 6x - 7?

• x + 7 and x - 1

• x - 7 and x + 1

• x + 6 and x - 7

• x - 6 and x + 7

When solving 2k^2 + 11k - 40 = 0 by factoring, what is the correct factorization?

• 2k - 5 and k + 8

• 2k + 5 and k - 8

• 2k - 8 and k + 5

• 2k + 8 and k - 5

How do you adjust an equation to standard form for factoring?

• Ensure the equation equals one

• Factor out the greatest common factor first

• Move all terms to one side to set the equation to zero

• Divide all terms by the leading coefficient

What is the first step in factoring a quadratic equation like x^2 - x - 2?

• Identify the coefficients a, b, and c

• Set the equation to equal one

• Divide each term by x

• Draw a graph of the equation

What is the significance of the x-intercepts in the context of quadratic equations?

• They represent the maximum values of the function

• They indicate where the graph crosses the y-axis

• They show the inflection points of the graph

• They represent the solutions to the equation when set to zero

What does factoring a quadratic equation help you find in its graph?

• The asymptotes

• The range

• The x-intercepts

• The vertex