Factoring Expressions Using Substitution

The video tutorial explains how to factor complex expressions using the method of substitution. It covers two examples: the first involves factoring x^4 - 8x^2 + 15 by substituting x^2 with a new variable, U, to simplify the expression into a quadratic form. The second example deals with factoring 2y^2 - 13y^4 + 21, which involves fractional exponents. The tutorial demonstrates the use of substitution and factor by grouping to achieve the final factored form in terms of the original variables.

What method is introduced for factoring expressions in the video?

• Substitution

• Completing the square

• Graphing

• Elimination

In the first example, what substitution is made to simplify the expression?

• U = x^3

• U = x

• U = x^2

• U = x^4

What is the factored form of the expression U^2 - 8U + 15?

• (U + 5)(U - 3)

• (U - 5)(U + 3)

• (U + 5)(U + 3)

• (U - 5)(U - 3)

What is the final factored form of x^4 - 8x^2 + 15 in terms of X?

• (x^2 - 5)(x^2 - 3)

• (x^2 - 5)(x^2 + 3)

• (x^2 + 5)(x^2 + 3)

• (x^2 + 5)(x^2 - 3)

What is the first step in handling the second example with fractional exponents?

• Finding a common denominator

• Using the quadratic formula

• Graphing the expression

• Completing the square

What substitution is made for the second example to simplify the expression?

• U = y^1/2

• U = y^1/5

• U = y^1/4

• U = y^1/3

What is the product of A and C in the second example?

• 84

• 42

• 13

• 21

Which method is used to factor the trinomial in the second example?

• Completing the square

• Synthetic division

• Factor by grouping

• Quadratic formula

What is the final factored form of the second example in terms of Y?

• (y^4 - 3)(2y^4 - 7)

• (y^4 + 3)(2y^4 + 7)

• (y^4 + 3)(2y^4 - 7)

• (y^4 - 3)(2y^4 + 7)

What is the purpose of using substitution in these examples?

• To simplify the expression to a familiar form

• To solve the equation directly

• To eliminate variables

• To change the degree of the polynomial