Question

Using the convolution approach with all the necessary steps, compute the product of A(x)=1-3 x² and B(x)=-3+6 x-7 x².

Answer 1

To find the product of A(x) and B(x) using the convolution method, multiply each term of the first polynomial by each term of the second polynomial and combine like terms to obtain -3 + 6x + 2x² - 18x³ + 21x⁴.

Step-by-step explanation:

To compute the product of A(x) and B(x) using the convolution approach, we multiply each term in the first polynomial by each term in the second polynomial and sum the results.

The first polynomial is A(x) = 1 - 3x² and the second is B(x) = -3 + 6x - 7x².

The steps are as follows:

1. Multiply the constant term in A(x) by each term in B(x):
   (1)(-3) + (1)(6x) + (1)(-7x²) = -3 + 6x - 7x²
2. Multiply the term -3x² in A(x) by each term in B(x):
   (-3x²)(-3) + (-3x²)(6x) + (-3x²)(-7x²) = 9x² - 18x³ + 21x⁴
3. Add the results from steps 1 and 2 to get the final polynomial:

-3 + 6x + (9x² - 7x²) - 18x³ + 21x⁴

The final result after combining like terms is:

-3 + 6x + 2x² - 18x³ + 21x⁴