Question

What happens to leading coefficients when you multiply or divide polynomials? It is the product or quotient (answer when you multiply/divide) of the leading coefficients from the original polynomials.

Answer 1

When you multiply or divide polynomials, the leading coefficients are multiplied or divided to find the leading coefficient of the resulting polynomial.

Step-by-step explanation:

When you multiply or divide polynomials, the leading coefficients are multiplied or divided to find the leading coefficient of the resulting polynomial.

For example, let's say we have two polynomials: 3x^2 + 5x + 2 and 2x^3 + 4x^2 + 6x + 8.

If we multiply these polynomials, we would get: (3x^2 + 5x + 2) * (2x^3 + 4x^2 + 6x + 8) = 6x^5 + 22x^4 + 38x^3 + 46x^2 + 38x + 16.

The leading coefficient of the original polynomial 3x^2 + 5x + 2 is 3, and the leading coefficient of the original polynomial 2x^3 + 4x^2 + 6x + 8 is 2. When we multiply them, the leading coefficients multiply together to get 6, which becomes the leading coefficient of the resulting polynomial.