Question

Two polynomial functions g and h are defined as g(x) = ax^3 + 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 function that represents g + h is the sum of the corresponding terms with the same degrees from each polynomial. The function is f(x) = ax^3 + (b + d)x^2 + (c - e)x, which corresponds to answer choice B.

Step-by-step explanation:

To find the function that represents g + h, we simply need to add together the corresponding terms from each function based on their degrees. Given:

• g(x) = ax^3 + bx^2 + cx
• h(x) = dx^2 - ex

We combine terms with the same power of x:

1. The cubic term will remain as is because h(x) has no cubic term. So we have ax^3.
2. For the quadratic term, we combine bx^2 and dx^2 to get (b + d)x^2.
3. For the x term, we combine cx and -ex to get (c - e)x.

Therefore, the function representing g + h is:

f(x) = ax^3 + (b + d)x^2 + (c - e)x

And the correct answer is B) f(x) = ax^3 + (b + d)x^2 + (c - e)x.