Substitution and Factoring Techniques

The video tutorial explains how to factor expressions using the method of substitution. It begins with an introduction to the method, highlighting the form ax^2 + bx + c. The first example demonstrates factoring an expression with fractional exponents by substituting a new variable. The second example involves factoring an expression with binomials, again using substitution. The tutorial emphasizes the importance of identifying the correct form and using substitution to simplify the factoring process.

What is the primary form an expression must resemble to use the method of substitution?

• ax^2 + bx + c

• ax^3 + bx + c

• ax^2 + bx^2 + c

• ax + bx + c

In the expression x^(2/5) + 3x^(1/5) - 40, what is the variable factor of the middle term?

• x^(2/5)

• x

• x^(1/5)

• x^2

What substitution is made for the variable factor in the first example?

• u = x^2

• u = x^(1/5)

• u = x^(2/5)

• u = x

What are the factors of negative 40 that add up to positive three in the first example?

• -8 and 5

• -6 and 7

• -4 and 10

• -5 and 8

In the second example, what substitution is made for the expression (x-3)?

• u = x+3

• u = x-3

• u = x

• u = x^2

What are the factors of positive 12 that add up to negative seven in the second example?

• -6 and -1

• -5 and -2

• 4 and 3

• -4 and -3

After substitution in the second example, what is the expression in terms of u?

• u^2 - 7u + 12

• u^2 + 7u + 12

• u^2 - 7u - 12

• u^2 + 7u - 12

What is the simplified form of the factor x-3-4?

• x-7

• x-1

• x-4

• x-6

What is the simplified form of the factor x-3-3?

• x-7

• x-4

• x-6

• x-5

What method is used to factor the expressions in the video?

• Substitution

• Elimination

• Graphing

• Completing the square