Q1. Factor the trinomial completely:

Background

Topic: Factoring Higher-Degree Polynomials

This question tests your ability to factor a quartic (degree 4) trinomial. The process often involves recognizing patterns and possibly using substitution to reduce the quartic to a quadratic form.

Key Terms and Formulas

• Quartic trinomial: A polynomial with three terms and the highest degree of 4.

• Factoring: Writing a polynomial as a product of simpler polynomials.

• Substitution: Sometimes, letting can help reduce the quartic to a quadratic.

Step-by-Step Guidance

1. Notice that can be rewritten in terms of . Let , so the expression becomes .

2. Now, factor as you would a quadratic trinomial. Look for two numbers that multiply to and add to .

3. Once you have factored the quadratic in terms of , substitute back for $x$ in each factor.

4. Check if each resulting factor can be further factored (for example, if you have a difference of squares).

Try solving on your own before revealing the answer!