Solving Quadratic Equations by Factoring

The video tutorial explains how to solve a quadratic equation by first converting it to standard form, then factoring it, and finally solving the factored equation to find the solutions. The process involves identifying the quadratic equation, rearranging it to standard form, factoring the trinomial, and solving the resulting mini equations to find the values of x that satisfy the original equation. The solutions are verified by substituting them back into the equation.

What is the standard form of a quadratic equation?

• ax + bx^2 = c

• ax^2 + bx = c

• ax^2 = bx + c

• ax^2 + bx + c = 0

What must be done to 'x^2 + 4x = 12' to transform it into standard form?

• Divide each side by 12

• Multiply each side by 12

• Subtract 12 from both sides

• Add 12 to both sides

Which pair of numbers multiplies to -12 and adds to 4?

• 4 and -3

• 2 and -6

• 3 and -4

• -2 and 6

What is the next step after factoring the equation 'x^2 + 4x - 12 = 0'?

• Combine like terms

• Subtract 4x from both sides

• Set each factor equal to zero

• Add 12 to both sides

What is the purpose of factoring in solving quadratic equations?

• To simplify the equation to linear form

• To find the roots of the equation

• To convert the quadratic to an exponential form

• To eliminate the variable x from the equation

What are the solutions to the equation 'x^2 + 4x - 12 = 0' after factoring and solving?

• x = 2 and x = 6

• x = 2 and x = -6

• x = -2 and x = 6

• x = -2 and x = -6

How do you solve the mini equation 'x - 2 = 0'?

• Add 2 to both sides

• Subtract 2 from both sides

• Subtract 2 from x

• Add 2 to x

What is the result of solving the equation 'x + 6 = 0'?

• x = 12

• x = 0

• x = -6

• x = 6

Which operation is used to solve the equation 'x + 6 = 0' for x?

• Subtraction

• Division

• Addition

• Multiplication

What does setting each factor of a factored quadratic equation equal to zero accomplish?

• It balances both sides of the equation

• It simplifies the equation

• It determines the possible values of x

• It finds the maximum value of x