Question

multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. determine the degree and maximum possible number of terms for the product of these trinomials: ((x^2 + x + 2)(x^2 - 2x + 3)). explain how you arrived at your answer.

Explanation:

Step1: Distribute first trinomial terms

$$(x^2 + x + 2)(x^2 - 2x + 3) = x^2(x^2 - 2x + 3) + x(x^2 - 2x + 3) + 2(x^2 - 2x + 3)$$

Step2: Expand each product

$$= x^4 - 2x^3 + 3x^2 + x^3 - 2x^2 + 3x + 2x^2 - 4x + 6$$

Step3: Combine like terms

$$= x^4 + (-2x^3 + x^3) + (3x^2 - 2x^2 + 2x^2) + (3x - 4x) + 6$$
$$= x^4 - x^3 + 3x^2 - x + 6$$

Step4: Find degree and max terms

Degree: Highest exponent is 4. Max terms: Multiply term counts ($3 \times 3 = 9$) before combining like terms.

Answer:

• Degree of the product: $4$
• Maximum possible number of terms before combining like terms: $9$
• Product of the trinomials: $x^4 - x^3 + 3x^2 - x + 6$