Solving and Factoring Polynomial Equations

The video tutorial explains how to factor and solve a polynomial equation. It begins by factoring out the greatest common factor (GCF) from the polynomial. The tutorial then focuses on factoring a challenging trinomial using the trial and error method. After successfully factoring the trinomial into binomial factors, the video demonstrates how to solve the equation by setting each factor to zero, resulting in three solutions. The tutorial provides a step-by-step approach to ensure understanding of the factoring and solving process.

What is the first step in factoring a polynomial equation?

• Combine like terms

• Use the quadratic formula

• Factor out the greatest common factor

• Identify the leading coefficient

Which method is suggested for factoring a challenging trinomial?

• Graphing

• Trial and error

• Completing the square

• Synthetic division

What are the possible first position factors for 20Z squared?

• 1Z and 20Z

• 2Z and 10Z

• All of the above

• 4Z and 5Z

What is the correct factorization of the trinomial 20Z^2 - 11Z - 3?

• (5Z - 3)(4Z + 1)

• (5Z + 1)(4Z - 3)

• (5Z - 1)(4Z + 3)

• (5Z + 3)(4Z - 1)

How many solutions does the factored polynomial equation have?

• One

• Three

• Two

• Four

What is the solution for the factor Z = 0?

• Z = 0

• Z = 1

• Z = -1

• Z = 1/5

How do you solve the equation 5Z + 1 = 0?

• Multiply both sides by 5

• Divide both sides by 1

• Subtract 1 from both sides and divide by 5

• Add 1 to both sides

What is the solution for the equation 5Z + 1 = 0?

• Z = 1/5

• Z = -1/5

• Z = 5

• Z = -5

What is the solution for the equation 4Z - 3 = 0?

• Z = 3/4

• Z = 4/3

• Z = -4/3

• Z = -3/4

What operation is performed first to solve 4Z - 3 = 0?

• Subtract 3 from both sides

• Add 3 to both sides

• Divide both sides by 4

• Multiply both sides by 4