Answer:
1. (h + p)(x) = 2x^2 - 11x + 16
2. It is the same problem as #1.
3. (k - f)(x) = 5x^3 + x^2 - 17x + 2
4. (q - g)(x) = 4x^2 + 7x - 14
Explanation:
(h + p)(x)
We are given that the values of h(x) = 2x^2 - 5x + 15 and p(x) = -6x + 1. Using these values you can substitute them into (h + p)(x).
(2x^2 - 5x + 15) + (-6x + 1)
Start by combining like terms. -5x and -6x will combine; 15 and 1 will also combine. 2x^2 will stay the same since there is no other term for it to combine with.
2x^2 - 11x + 16
Combine like terms. We will be adding since h(x) and p(x) are being added together.
(k - f)(x)
We are given that k(x) = 8x^3 - 12x + 2 and f(x) = 3x^3 - x^2 + 5x. Knowing these values we can substitute k(x) and f(x) into (k - f)(x). This will look like:
(8x^3 - 12x + 2) - (3x^3 - x^2 + 5x)
Start by combining like terms. The terms to the same power can be combined (keep in mind we are finding the difference, in other words: subtracting). The terms with "x" can be combined as well. After doing so, your evaluated expression will look like:
5x^3 + x^2 - 17x + 2
(q - g)(x)
q(x) = 4x^2 + 9x - 10 and g(x) = 2x + 4. Substitute q(x) and g(x) into (q - g)(x).
(4x^2 + 9x - 10) - (2x + 4)
Use the same rules I said above. The simplified expression will look like:
4x^2 + 7x - 14