Factoring Polynomials and Equations

The video tutorial covers the process of factoring polynomials and demonstrates its usefulness in solving polynomial equations. It begins with an introduction to the concept of factoring, followed by detailed examples of factoring polynomials. The tutorial then explains how factoring can be applied to solve polynomial equations, highlighting the importance of finding solutions or roots. The video concludes with a demonstration of solving a factored polynomial equation, emphasizing the practical application of these techniques.

What is the first step in factoring the polynomial 3x^3 - 21x?

• Multiply by x

• Add 21x

• Factor out 3x

• Divide by 3

When factoring 4x^3 + 10x^2 - 2x, what common factor is taken out?

• x^2

• 2x

• 4x

• 10x

Why is factoring polynomials useful?

• It simplifies addition

• It helps solve polynomial equations

• It makes multiplication easier

• It reduces the degree of the polynomial

In the equation 9x^2 = 27x, what is the first step to solve it by factoring?

• Divide both sides by x

• Multiply both sides by 9

• Add 27x to both sides

• Subtract 27x from both sides

What are the solutions to the equation 9x(x - 3) = 0?

• x = 0 and x = -3

• x = 3 and x = -9

• x = 9 and x = -3

• x = 0 and x = 3

How do you solve the equation 4a^2 + a = 0 by factoring?

• Add 1 to both sides

• Factor out 4a

• Factor out a

• Subtract a from both sides

What is the solution for a in the equation a(4a + 1) = 0?

• a = 0 and a = 1/4

• a = 0 and a = -1/4

• a = 1 and a = -1/4

• a = 1 and a = 1/4

In the equation (x - 5)(2x + 7)(3x - 4) = 0, what is one of the solutions for x?

• x = 7

• x = -5

• x = -7

• x = 5

What is the solution for x in the factor 2x + 7 = 0?

• x = -2/7

• x = 2/7

• x = -7/2

• x = 7/2

What is the solution for x in the factor 3x - 4 = 0?

• x = -3/4

• x = 3/4

• x = -4/3

• x = 4/3