How to simplify a trigonometric expression by factoring

The video tutorial explains the process of factoring expressions, starting with a quadratic example and extending to higher-degree polynomials. It then applies the same principles to trigonometric expressions involving cosines, demonstrating how to simplify them using trigonometric identities. The tutorial emphasizes understanding the underlying concepts of factoring and simplification.

What is the result of factoring the expression X^2 - 2X + 1?

• (X - 2)(X + 1)

• (X + 1)(X + 1)

• (X - 1)(X - 1)

• (X - 1)(X + 1)

When factoring X^4 - 2X^2 + 1, what are the factors?

• (X^2 - 1)(X^2 - 1)

• (X^2 - 2)(X^2 + 1)

• (X^2 - 1)(X^2 + 1)

• (X^2 + 1)(X^2 + 1)

How can the expression cosine^4(X) - 2cosine^2(X) + 1 be factored?

• (cosine^2(X) + 1)(cosine^2(X) + 1)

• (cosine^2(X) - 1)(cosine^2(X) + 1)

• (cosine^2(X) - 2)(cosine^2(X) + 1)

• (cosine^2(X) - 1)(cosine^2(X) - 1)

What identity is used to simplify cosine^2(X) - 1?

• sine^2(X) + cosine^2(X) = 1

• sine^2(X) - cosine^2(X) = 1

• cosine^2(X) - sine^2(X) = 1

• cosine^2(X) + sine^2(X) = 0

What is the final expression after factoring and simplifying cosine^4(X) - 2cosine^2(X) + 1?

• -sine^4(X)

• cosine^4(X)

• -cosine^4(X)

• sine^4(X)