Factoring and Solving Equations

The video tutorial explains how to factor the quadratic equation x^2 + 14x + 48. It begins by setting up a skeleton equation and identifying the signs. The instructor then finds factors of 48 that add up to 14, specifically 6 and 8. The factorization is verified using the FOIL method. Finally, the video demonstrates solving for X values, showing that X equals -6 or -8, and confirms these results using the quadratic equation.

What is the first step in factoring the equation x^2 + 14x + 48?

• Find the roots of the equation

• Set up a skeleton equation

• Use the quadratic formula

• Multiply all terms by 2

Which pair of numbers multiplies to 48 and adds up to 14?

• 7 and 7

• 6 and 8

• 5 and 9

• 4 and 12

What method is used to verify the factored form of the equation?

• Substitution method

• Completing the square

• FOIL method

• Graphing method

What is the result of combining 8x and 6x in the FOIL method?

• 12x

• 2x

• 48x

• 14x

After factoring, what are the possible values of x?

• x = -6 and x = 8

• x = -6 and x = -8

• x = 6 and x = 8

• x = 6 and x = -8

What equation do you get when you set x + 6 to zero?

• x = 6

• x = -6

• x = 0

• x = 12

What equation do you get when you set x + 8 to zero?

• x = 8

• x = 16

• x = -8

• x = 0

What is the purpose of setting each factor to zero?

• To find the axis of symmetry

• To find the y-intercept

• To find the x-intercepts

• To find the vertex

Which method can also confirm the solutions found by factoring?

• Graphing

• Quadratic formula

• Synthetic division

• Completing the square

What is the final step in confirming the factored equation?

• Checking with a calculator

• Using the quadratic formula

• Rewriting the equation

• Graphing the equation