Q:

Describing the Structure of the Product of Two Trinomials 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.

Accepted Solution

A:
hello

There will be 5 terms (monomials), after these trinomials are multiplied.Degree of obtained polynomial will be 4 (the highest exponent).-----------------------------------------------------------------Working procedure:(x^2 + x + 2) * (x^2 - 2*x + 3) =(each addend in first parentheses you multiply with each addend in the second one):= x^2*x^2 - x^2*2*x + x^2*3  + x*x^2 - x*2*x + x*3  + 2*x^2 - 2*2*x + 2*3 =Now, we multiply these small terms:= x^4 - 2*x^3 + 3*x^2 + x^3 - 2*x^2 + 3*x + 2*x^2 - 4*x + 6 =Now, we add and subtract the like terms (the ones with same exponent):= x^4 - x^3 + 3*x^2 - x + 6And this is the final solution, simplified product of these two parentheses. 
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