Factoring and Solving Equations

This video tutorial covers solving quadratic equations using the factor by grouping technique. It begins with an introduction to the method, followed by a detailed walkthrough of two examples. The first example demonstrates factoring a quadratic equation with a common binomial factor, leading to solutions for the equation. The video then reviews the factor by grouping technique, emphasizing its use for polynomials with four or six terms. A second, more complex example is provided, illustrating the process of factoring and solving for the roots of the equation. The tutorial concludes with a brief overview of what to expect in the next video.

What is the first step in solving a quadratic equation using the factor by grouping technique?

• Divide the polynomial into two parts

• Multiply all terms by a constant

• Add a constant to both sides

• Subtract a constant from both sides

When a product of factors equals zero, what can be concluded about the factors?

• At least one factor must be zero

• The factors are negative

• The factors are equal

• All factors must be non-zero

What is the purpose of dividing the polynomial in half during the factor by grouping process?

• To eliminate terms

• To identify a common binomial factor

• To find the greatest common factor

• To simplify the equation

In the example given, what is the greatest common factor of 3x^2 + 6x?

• x

• 3x

• 3

• 6

After factoring out the common binomial factor, what is the next step in solving the equation?

• Divide the factors

• Set each factor equal to zero

• Multiply the factors

• Add the factors

What is the solution to the equation 3x + 4 = 0?

• x = 4/3

• x = -4/3

• x = -3/4

• x = 3/4

What is the common binomial factor in the example of 4x and 8?

• x - 2

• x + 2

• x + 4

• x - 4

What is the result of factoring out 3x from 3x^2 + 6x?

• x + 6

• x + 4

• x + 3

• x + 2

What is the solution to the equation x + 2 = 0?

• x = 1

• x = -2

• x = 2

• x = 0

What will be covered in the next video?

• Introduction to linear equations

• More examples of factor by grouping

• Graphing quadratic functions

• Advanced calculus techniques