Solving Quadratic Equations through Factoring Techniques

This video tutorial focuses on solving word problems involving quadratic equations, specifically using the factoring method. It begins with an introduction to the topic, followed by detailed walkthroughs of several problems, including finding the dimensions of rectangles and adjusting for borders. Each problem is solved step-by-step, emphasizing the importance of setting equations to zero and factoring to find solutions. The video encourages viewers to pause and attempt problems independently before revealing solutions.

What is the formula for the area of a rectangle?

• Length + Width

• Length / Width

• Length - Width

• Length * Width

What does 'triple the width' imply in the context of the rectangle's length?

• Three times the width

• Width minus three

• Width divided by three

• Width plus three

How do you set a quadratic equation to zero for solving?

• Add the constant term

• Multiply by the leading coefficient

• Subtract the constant term

• Divide by the leading coefficient

What is the correct width of the rectangle if one solution is negative?

• 10 cm

• 8 cm

• 6 cm

• 4 cm

What happens to the area of the original rectangle when a uniform border is added?

• It remains the same

• It is halved

• It is doubled

• It is tripled

What expression represents the new width of the rectangle with the border?

• X + 6

• 2X + 6

• 2X + 20

• X + 20

How do you solve a quadratic equation after setting it to zero?

• By adding terms

• By factoring

• By subtracting terms

• By dividing terms

What is the new length of the rectangle after adding the border?

• 10 inches

• 12 inches

• 24 inches

• 20 inches

Which solution for X is acceptable for the dimensions of a rectangle?

• X = 2

• X = -2

• X = -15

• X = 0

What is the new width of the rectangle after solving the quadratic equation?

• 16 inches

• 10 inches

• 12 inches

• 14 inches