The video tutorial explains how to use substitution to simplify an expression by letting U equal the cotangent of X. It then demonstrates rewriting the expression in terms of U, factoring it by ensuring all terms are positive, and finally replacing U with the cotangent of X to achieve the final factored form.

What substitution is made at the beginning of the problem?

• U equals the cosine of X

• U equals the tangent of X

• U equals the cotangent of X

• U equals the sine of X

What is the expression rewritten in terms of U?

• 2U^2 + 3U + 1

• 2U^2 + U + 3

• U^2 + 2U + 3

• 3U^2 + 2U + 1

Which pair of terms multiply to give a positive one in the expression?

• Positive one and negative one

• Negative one and negative one

• Positive one and positive one

• Negative one and positive one

What is the final step to obtain the factored form?

• Replace U with cotangent of X

• Replace U with tangent of X

• Replace U with sine of X

• Replace U with cosine of X

What is the final factored form of the expression?

• 2(cotangent of X)^2 + 3(cotangent of X) + 1

• (2U + 1)(U + 1)

• (2(cotangent of X) + 1)(cotangent of X + 1)

• 2U^2 + 3U + 1