Factoring a trinomial when it is raised to the fourth power

The video tutorial explains the process of factoring polynomials, emphasizing the importance of identifying the greatest common factor (GCF) first. It demonstrates factoring using the box method and provides an example problem involving X^2. The tutorial progresses to more advanced factoring with X^4, explaining how to handle middle terms. The session concludes with verifying the factored form and ensuring the original problem is obtained.

What is the first step you should take when factoring a polynomial?

• Factor out the Greatest Common Factor (GCF)

• Identify the highest power of X

• Combine like terms

• Use the quadratic formula

What is the result of factoring out the GCF of 7 from the polynomial 7X^4 + 56X^2 + 49?

• 7X^4 + 8X^2 + 7

• X^4 + 8X^2 + 7

• 7(X^4 + 8X^2 + 7)

• X^4 + 56X^2 + 49

When using the box method, what is the purpose of creating a box?

• To identify the GCF

• To visualize the distribution of terms

• To simplify multiplication

• To organize terms for addition

In the expression X^4 + 8X^2 + 7, what are the two binomials it factors into?

• X^2 + 4 and X^2 + 3

• X^2 + 8 and X^2 + 7

• X + 7 and X + 1

• X^2 + 7 and X^2 + 1

Why is it important to verify your factorization by multiplying the factors back together?

• To confirm the original expression is correct

• To ensure the factors are in simplest form

• To simplify the expression further

• To check for calculation errors