Final answer:
The degree of the polynomial is 8, which is found by multiplying the individual polynomials and identifying the highest power of x after simplification. Option (A) Polynomial with degree 8 is the correct answer.
Step-by-step explanation:
To determine the degree of the polynomial y = (0.2x³ - 0.3x² + 0.1)(-0.1x⁵ + 0.4x² - 4) + 0.3, we must first look at the given expression and perform the necessary multiplication. The degree of a polynomial is the highest power of the variable x that appears in the polynomial after it has been simplified.
The expression given is a product of two polynomials and a constant. To find the degree of the overall polynomial, we can identify the individual degrees of the polynomials in the product. The first polynomial, 0.2x³ - 0.3x² + 0.1, is of degree 3 because the highest power of x is 3. The second polynomial, -0.1x⁵ + 0.4x² - 4, is of degree 5 because the highest power of x is 5.
When multiplying these two polynomials together, the degrees of the individual terms will add together. Therefore, the highest degree term will come from the multiplication of the highest degree terms in each polynomial: 0.2x³ * -0.1x⁵, which will give us an x to the power of 3+5, or x⁸. Thus, the combined polynomial will be of degree 8.
The constant term + 0.3 does not change the degree of the polynomial as it does not contain the variable x. Therefore, the resulting polynomial's degree is still 8, making the answer (A) Polynomial with degree 8.