Final answer:
To find f(x) + g(x), add the two polynomials. The resulting polynomial has a degree of 6 and 4 different terms. To find h(x) - j(x), subtract the two polynomials. The resulting polynomial has a degree of 4 and 4 different terms.
Step-by-step explanation:
To find f(x) + g(x), we simply add the two given functions.
Given:
- f(x) = 6x^2 + 7x
- g(x) = -2x^6 + 9x + 5
Adding them together:
f(x) + g(x) = (6x^2 + 7x) + (-2x^6 + 9x + 5)
Simplifying further, we combine like terms:
f(x) + g(x) = -2x^6 + 6x^2 + 16x + 5
The degree of the polynomial -2x^6 + 6x^2 + 16x + 5 is 6. The number of different terms is 4.
To find h(x) - j(x), we subtract the two given functions.
Given:
- h(x) = 4x^3 + 6x^2 + 1
- j(x) = -8x^4 + 5x^2 + 6
Subtracting them:
h(x) - j(x) = (4x^3 + 6x^2 + 1) - (-8x^4 + 5x^2 + 6)
Simplifying further, we combine like terms:
h(x) - j(x) = 8x^4 - 4x^3 + x^2 - 5
The degree of the polynomial 8x^4 - 4x^3 + x^2 - 5 is 4. The number of different terms is 4.