Solving Quadratics by Factoring: Day 1 Challenge

Mrs. Versales introduces solving quadratic equations by factoring, emphasizing the zero product property. The lesson includes four examples: solving equations already in factored form, factoring with the greatest common factor, expanding expressions, and factoring quadratic expressions. Each example demonstrates the step-by-step process to find solutions, reinforcing the concepts of factoring and the zero product property.

What is the primary goal when solving quadratic equations by factoring?

• To eliminate all variables

• To simplify the equation

• To convert the quadratic into a linear equation

• To find the value of x that makes the equation true

According to the zero product property, what can be concluded if a product of two factors equals zero?

• The equation has no solution

• At least one of the factors must be zero

• Both factors must be zero

• The factors are undefined

In the equation (x + 6)(x - 7) = 0, what are the solutions for x?

• x = -6 and x = -7

• x = -6 and x = 7

• x = 6 and x = 7

• x = 6 and x = -7

How do you solve the equation 2x(3x + 9) = 0 using the zero product property?

• Divide 2x by 3x + 9 and set the quotient to zero

• Set 2x = 0 and solve, then set 3x + 9 = 0 and solve

• Multiply 2x and 3x + 9 and set the result to zero

• Add 2x and 3x + 9 and set the sum to zero

What is the solution for x in the equation 2x = 0?

• x = 2

• x = 0

• x = -2

• x = 1

When solving (x + 1)^2 = 0, why is there only one unique solution?

• Because both factors are the same

• Because the equation is non-quadratic

• Because the factors are complex numbers

• Because the equation has no real solutions

What steps are necessary to solve the equation x^2 + 8x + 15 = 0?

• Factor the quadratic, then apply the zero product property

• Use the quadratic formula

• Graph the equation and find the x-intercepts

• Isolate x on one side of the equation

Which pair of numbers multiplies to 15 and adds up to 8?

• 4 and 11

• 2 and 7

• 3 and 5

• 1 and 15

What is the solution for x in the equation x + 3 = 0?

• x = 1

• x = -3

• x = 0

• x = 3

After factoring the quadratic x^2 + 8x + 15, what should you do next to find the solutions for x?

• Apply the zero product property

• Integrate the equation

• Differentiate each term

• Combine like terms