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). Explain how you arrived at your answer.
Answers
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.
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To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x2 by x2, you add the exponents to get x4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.
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