multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial…

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.

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.

Answer

Explanation:

Step1: Recall degree - rule for polynomial multiplication

The degree of a polynomial is the highest power of the variable. When multiplying two non - zero polynomials (P(x)) and (Q(x)) of degrees (m) and (n) respectively, the degree of the product (P(x)Q(x)) is (m + n). The degree of (x^{2}+x + 2) is (2) and the degree of (x^{2}-2x + 3) is (2). So the degree of the product is (2+2=4).

Step2: Recall term - rule for polynomial multiplication

When multiplying a polynomial with (m) terms by a polynomial with (n) terms, the maximum number of terms in the product before combining like - terms is (m\times n). Here, (m = 3) (since (x^{2}+x + 2) has 3 terms) and (n = 3) (since (x^{2}-2x + 3) has 3 terms). So the maximum number of terms before combining like - terms is (3\times3=9).

Answer:

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