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: (x2 + x + 2)(x2 – 2x + 3).HOW DO I Explain how it arrived at your answer?

Answer 1

The correct answer is:

The degree of the polynomial is 4 and the maximum number of terms is 9.

Explanation:

Multiplying the terms of each trinomial that have the largest degree, we are multiplying x²(x²); this gives us x⁴.  This means the degree of the trinomial, the largest degree of all terms, is 4.

Without multiplying through, we know we will multiply each term of the first trinomial by each term of the second one.  This means that, if no terms are like to combine, we could have 3(3) = 9 terms.

Answer 2

For this case we have the following trinomial product:
 $(x ^ 2 + x + 2) (x ^ 2 - 2x + 3)$
 By doing distributive property we have:
 $(x ^ 4 - 2x ^ 3 + 3x ^ 2) + (x ^ 3 - 2x ^ 2 + 3x) + (2x ^ 2 - 4x + 6)$
 Grouping similar terms we have:
 $x ^ 4 + x ^ 3 (-2 + 1) + x ^ 2 (3-2 + 2) + x (3-4) + (6)$
 Adding terms of the same exponent we have:
 $x ^ 4 - x ^ 3 + 3x ^ 2 - x + 6$
 Answer:
 $x ^ 4 - x ^ 3 + 3x ^ 2 - x + 6$
 The degree of polynomial is equal to 4
 The maximum number of terms is equal to 5.