Question

Two polynomial functions g and h are defined as g(x) = ax + bx^2 + cx and h(x) = dx^2 - ex.

Which function represents g + h?


A) f(x) = ax^3 + (bd)x^2 - (ce)x
B) f(x) = ax^3 + (b + d)x^2 + (c - e)x
C) f(x) = ax^3 + (b + d)x^2 + (c + e)x
D) f(x) = (a + d)x^5 + (b - e)x^3 + cx

Answer 1

The sum of the two polynomial functions g and h is obtained by adding the corresponding terms of each function. So, if g(x) = ax + bx^2 + cx and h(x) = dx^2 - ex, then g(x) + h(x) would be (ax + bx^2 + cx) + (dx^2 - ex).

This simplifies to ax + (b + d)x^2 + cx - ex, which can be rearranged to (b + d)x^2 + ax + (c - e)x.

So, the correct answer is B) f(x) = (b + d)x^2 + ax + (c - e)x. Please note that the terms in the polynomial may not always be written in the same order, but the coefficients of the corresponding terms should match.