Factoring Quadratics: Techniques and Shortcuts

What is the primary goal when starting to factor a quadratic expression?

• Graphing the quadratic expression

• Determining the highest common factor

• Solving the quadratic equation for x

• Finding two numbers that multiply to the last number and add to the second number

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

• 1 and -12

• -1 and 12

• -2 and 6

• 2 and -6

Which of the following is a correct factored form of X^2 + 4X - 12?

• X + 2 and X - 6

• X + 6 and X - 2

• X - 6 and X + 2

• X - 2 and X + 6

How can you simplify the expression 3X^2 + 12X - 36?

• By using the 'Magic X' method

• By applying the quadratic formula

• By completing the square

• By dividing each term by 3

What does pulling out an overall constant from a quadratic expression help with?

• Calculating its discriminant

• Changing the shape of its graph

• Simplifying the expression for easier factoring

• Increasing the complexity of the problem

What is the first step in the 'Magic X' method?

• Multiplying the leading coefficient by the constant term

• Finding the roots of the quadratic equation

• Drawing an X and placing the product of the first and last coefficients at the top

• Listing all possible pairs of factors

What do the numbers at the top and bottom of the 'Magic X' represent?

• Randomly chosen numbers for trial and error

• The product of the first and last coefficients, and the middle coefficient

• The solutions to the quadratic equation

• The coefficients of the quadratic equation

How do you use the numbers found with the 'Magic X' method?

• By substituting them into the quadratic formula

• By adding them to the quadratic equation

• By graphing them on a coordinate plane

• By dividing them by the leading coefficient

What is the purpose of checking your factoring by foiling?

• To ensure the factored form simplifies back to the original quadratic

• To graph the quadratic expression

• To find the roots of the quadratic equation

• To determine if the quadratic is prime

After applying the 'Magic X' method, what do the fractions represent?

• The exponents in the factored form

• The solutions to the quadratic equation

• The new factors of the quadratic expression

• The coefficients of the original quadratic