Question

Write each polynomial in descending order.

(4x² + 1) as (4x² + 1).

[7x⁵ + 1.5x³ + 2x]

Answer 1

The product of the polynomials (4x² + 1) and (7x⁵ + 1.5x³ + 2x) when multiplied and combined like terms result in 28x⁷ + 13x⁵ + 9.5x³ + 2x, which is written in descending order.

Step-by-step explanation:

The student has asked about writing the product of two polynomials in descending order. The specific polynomial expressions to multiply are (4x² + 1) and (7x⁵ + 1.5x³ + 2x). To do this, we need to individually multiply each term in the first polynomial by each term in the second polynomial and then combine like terms, ensuring that the final expression is written with the powers of x in descending order.

To multiply the polynomials, we distribute each term in the first polynomial across the second polynomial:

(4x²)(7x⁵) = 28x⁷

(4x²)(1.5x³) = 6x⁵

(4x²)(2x) = 8x³

(1)(7x⁵) = 7x⁵

(1)(1.5x³) = 1.5x³

(1)(2x) = 2x

Now, combine like terms to get the polynomial in descending order:

28x⁷ + (6+7)x⁵ + (8+1.5)x³ + 2x

Which simplifies to:

28x⁷ + 13x⁵ + 9.5x³ + 2x

This is the product of the two polynomials, written in descending order.