Question

018-2019) Q4

Describing the structure on the TTO
HE
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

`\boxed{\text{Degree = 4; Max. no. of terms = 5}}`

Explanation:

(x² + x + 2)(x² – 2x + 3)

1. Degree of product

The degree of the product of two polynomials is the sum of their degrees.

Each polynomial is of degree 2, so the degree of the product is 4.

That is, the term of highest degree must come from x² × x² = x⁴.

2. Maximum number of terms

The maximum number of terms is one more than the degree of the product.

Thus, there is a maximum of five terms in the product: one for each power of x plus a constant term.

P = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅