Factoring Trinomials and Expressions

The video tutorial explains how to factor complex expressions using substitution. It covers two examples: one involving X to the fourth power and another with fractional exponents. The method involves substituting variables to simplify the expressions into more familiar forms, factoring them, and then substituting back to the original variables.

What method is introduced for factoring expressions in this tutorial?

• Long division

• Substitution

• Synthetic division

• Completing the square

In the expression X^4 - 8X^2 + 15, what substitution is made to simplify the factoring process?

• U = X^4

• U = X^3

• U = X

• U = X^2

What are the factors of the trinomial 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)

In the second example, what is the common denominator used for the fractional exponents?

• 1/2

• 1/4

• 2/4

• 3/4

What substitution is made for the expression 2Y^(1/2) - 13Y^(1/4) + 21?

• U = Y^(1/2)

• U = Y^2

• U = Y^(1/4)

• U = Y

What is the product of A and C in the trinomial 2U^2 - 13U + 21?

• 2

• 13

• 42

• 21

Which method is used to factor the trinomial 2U^2 - 13U + 21?

• Factor by grouping

• Synthetic division

• Long division

• Completing the square

What are the factors of the trinomial 2U^2 - 13U + 21?

• (U + 3)(2U - 7)

• (U - 3)(2U + 7)

• (U + 3)(2U + 7)

• (U - 3)(2U - 7)

What is the final factored form of 2Y^(1/2) - 13Y^(1/4) + 21 in terms of Y?

• (Y^(1/4) - 3)(2Y^(1/4) - 7)

• (Y^(1/4) + 3)(2Y^(1/4) + 7)

• (Y^(1/4) - 3)(2Y^(1/4) + 7)

• (Y^(1/4) + 3)(2Y^(1/4) - 7)