Solving Polynomials in Factored Form

The video tutorial covers solving polynomial equations in factored form, emphasizing the zero product property. It explains how to set equations to zero and solve for roots or solutions. The tutorial also delves into factoring techniques, including finding the greatest common factor, and applies these methods to solve equations. Advanced examples are provided to reinforce understanding.

What does the zero product property state?

• If a product of two numbers is zero, one number must be negative.

• If a product of two numbers is zero, one or both of the numbers must be zero.

• If a product of two numbers is zero, both numbers must be positive.

• If a product of two numbers is zero, both numbers must be non-zero.

When solving the equation (x - 6)(x + 5) = 0, what are the possible values of x?

• x = 6 or x = -5

• x = -6 or x = 5

• x = 0 or x = 5

• x = 6 or x = 0

What is the first step in factoring a polynomial using the GCF method?

• Identify the smallest variable.

• Identify the largest variable.

• Identify the smallest number.

• Identify the largest number.

In the expression 15x and 20y, what is the greatest common factor?

• 3

• 5

• 20

• 15

What is the result of factoring 12y^2 - 21y using the GCF method?

• 3y(4y - 7)

• 3y(4y + 7)

• 4y(3y + 7)

• 4y(3y - 7)

What is the first step in solving the equation 10x^2 - 15x = 0?

• Divide by 10.

• Subtract 10x^2 from both sides.

• Add 15x to both sides.

• Factor out the GCF.

What are the solutions to the equation 5x = 0?

• x = 5

• x = 0

• x = -5

• x = 1

In the equation 6w^2 - 12w = 0, what is the GCF?

• 6w

• 12w

• 6

• 12

What is the result of factoring 9y^2 - 15y using the GCF method?

• 9y(3y - 5)

• 3y(3y + 5)

• 9y(3y + 5)

• 3y(3y - 5)

What are the solutions to the equation 3y - 5 = 0?

• y = 5/3

• y = 0

• y = 1

• y = 3/5