Factoring a trinomial by substituting x squared for x to the 4th power

The video tutorial explains how to factor a trinomial of the form X^4 + 7X^2 + 6. The instructor begins by addressing common student difficulties with higher order polynomials and introduces a substitution method to simplify the problem. By substituting X^2 for X^4, the trinomial is rewritten in a more familiar quadratic form. The instructor then demonstrates the factoring process and verifies the solution using the FOIL method. The tutorial concludes with a recap of the steps and the importance of understanding polynomial factoring.

What is the initial step in factoring a trinomial with higher order polynomials?

• Substitute X to the 4th with X squared

• Divide the equation by X

• Multiply all terms by 2

• Add 5 to each term

How do you rewrite the equation to make it easier to factor?

• By adding 10 to each term

• By substituting X squared for X to the 4th

• By multiplying each term by 3

• By dividing each term by 2

Which two numbers multiply to give 6 and add to give 7 in the factorization process?

• 2 and 3

• 3 and 4

• 1 and 6

• 2 and 5

What method is used to verify the factorization of the polynomial?

• The FOIL method

• The quadratic formula

• Completing the square

• Synthetic division

What is the final form of the factored polynomial?

• X^2 + 6X^2 + 6

• X^2 + 6X^2 + 1

• X^2 + 7X + 6

• X^2 + 6X + 1