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). Explain how you arrived at your answer.

Answer 1

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.

The degree of the product of the trinomials is 4 because the degree of each trinomial is 2.

The maximum number of terms in the product of the trinomials is 5.

There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.

Step-by-step explanation:

This is the response on Edge 2020-21. Hope this helps, have a great day!

Answer 2

Answer: Degree of polynomial (highest degree) =4

Maximum possible terms =9

Number of terms in the product = 5

Step-by-step explanation:

A trinomial is a polynomial with 3 terms.

The given product of trinomial:
`(x^2 + x + 2)(x^2 - 2x + 3)`

By using distributive property: a(b+c+d)= ab+ac+ad

`(x^2 + x + 2)(x^2 - 2x + 3)=(x^2 + x + 2) x^2+(x^2 + x + 2) (-2x)+(x^2 + x + 2)(3)\\\\=x^2(x^2)+x(x^2)+2(x^2)+x^2 (-2x)+x (-2x)+2 (-2x)+x^2 (3)+x (3)+2 (3)\\\\\\=x^4+x^3+2x^2-2x^3-2x^2-4x+3x^2+3x+6`

Maximum possible terms =9

Combine like terms

`x^4+x^3-2x^3+3x^2-4x+3x+6\\\\=x^4-x^3+3x^2-x+6`

Hence,
`\left(x^2\:+\:x\:+\:2\right)\left(x^2\:-\:2x\:+\:3\right)=x^4-x^3+3x^2-x+6`

Degree of polynomial (highest degree) =4

Number of terms = 5