Question

Let V(x)=−x²+2x−4 and W(x)=−x³+2x²+x+5. Find V(x)−W(x). .

Answer 1

You perform subtraction between the functions V(x) and W(x) by subtracting the corresponding terms in them. The equation resulting from subtracting the functions x³ - 3x² + x - 9.

Step-by-step explanation:

In mathematics, subtraction between two functions, V(x) and W(x), means subtracting the corresponding terms in them. Given the functions, V(x)=−x²+2x−4 and W(x)=−x³+2x²+x+5, we start with the highest power of x and work down to the constant. So, to find V(x) - W(x), you simply perform the subtraction term-by-term:

1. The cubic term of V(x) is 0 and that of W(x) is -x³. So the cubic term of V(x) - W(x) is 0 - (-x³) = x³.
2. The squared term in V(x) is -x² and in W(x) is 2x². So the squared term in V(x) - W(x) is -x² - 2x² = -3x².
3. The x term in V(x) is 2x and in W(x) is x. So the x term in V(x) - W(x) is 2x - x = x.
4. The constant term in V(x) is -4 and in W(x) is 5. So the constant term in V(x) - W(x) is -4 - 5 = -9.

Consequently, V(x) - W(x) = x³ - 3x² + x - 9.

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