Factoring and Completing the Square

The video tutorial covers solving quadratic equations using different methods. It starts with solving x^2 + x = 42 by factoring, then moves on to completing the square for x^2 - 8x = 5. The tutorial also demonstrates solving x^2 + 6x = 16 by factoring and concludes with factoring 2x^2 - 5x + 3 = 0. Each section explains the steps involved in solving these equations, emphasizing understanding over memorization.

What is the first step in solving a quadratic equation by factoring?

• Divide both sides by a constant

• Multiply both sides by a constant

• Add a constant to both sides

• Set the equation to zero

When factoring the equation x^2 + x - 42 = 0, what are the two numbers that multiply to -42 and add to 1?

• 6 and 7

• -7 and 6

• 7 and -6

• -6 and -7

What is the correct factorization of the equation x^2 + x - 42 = 0?

• (x - 7)(x + 6)

• (x - 6)(x + 7)

• (x + 7)(x - 6)

• (x + 6)(x - 7)

What is the purpose of completing the square in a quadratic equation?

• To simplify the equation

• To transform it into a perfect square trinomial

• To eliminate the constant term

• To factor the equation

In the equation x^2 - 8x = 5, what value should be added to both sides to complete the square?

• 8

• 16

• 2

• 4

What is the result of factoring the equation x^2 + 6x - 16 = 0?

• (x + 4)(x - 4)

• (x + 6)(x - 6)

• (x - 8)(x + 2)

• (x + 8)(x - 2)

Which of the following is a step in completing the square for the equation x^2 + 4x = 6?

• Divide both sides by 2

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply both sides by 2

What is the solution to the equation x^2 + 4x = 6 after completing the square?

• x = 2 or x = -2

• x = 5 or x = -5

• x = 1 or x = -1

• x = 3 or x = -3

What is the factorization of the equation 2x^2 - 5x + 3 = 0?

• (2x - 3)(x - 1)

• (2x + 3)(x + 1)

• (2x - 1)(x - 3)

• (2x + 1)(x + 3)

In the equation 2x^2 - 5x + 3 = 0, what are the signs of the factors?

• Both negative

• Both positive

• One positive, one negative

• One negative, one positive