Question

maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer. 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: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer.

Answer 1

Answer:

Sample Response: 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.

Answer 2

Degree = 4

Maximum possible number of terms for = 5

Solution:

Given expression:

$\left(x^{2}+x+2\right)\left(x^{2}-2 x+3\right)$

To multiply the trinomial by a trinomial:

$\left(x^{2}+x+2\right)\left(x^{2}-2 x+3\right)$

Multiply each of the first term by the each of the second term.

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

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

Remove the brackets and arrange the terms with same powers together.

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

            $=x^{4}- x^3+3x^2- x+6$

The product of the trinomials is $x^{4}- x^3+3x^2- x+6$.

Degree is the highest power of the variable.

Degree = 4

Maximum possible number of terms for = 5