To find $(g - f)(x)$, we need to subtract $f(x)$ from $g(x)$.

Given: $f(x) = 4x^3 + 3x^2 - 5x + 20$ $g(x) = 9x^3 - 4x^2 + 10x - 55$

Step 1: Subtract $f(x)$ from $g(x)$

$(g - f)(x) = g(x) - f(x)$ Substitute $f(x)$ and $g(x)$: $(g - f)(x) = (9x^3 - 4x^2 + 10x - 55) - (4x^3 + 3x^2 - 5x + 20)$

Step 2: Distribute the Negative Sign

$= 9x^3 - 4x^2 + 10x - 55 - 4x^3 - 3x^2 + 5x - 20$

Step 3: Combine Like Terms

• For $x^3$: $9x^3 - 4x^3 = 5x^3$
• For $x^2$: $-4x^2 - 3x^2 = -7x^2$
• For $x$: $10x + 5x = 15x$
• Constant terms: $-55 - 20 = -75$

Putting it all together: $(g - f)(x) = 5x^3 - 7x^2 + 15x - 75$

Answer

The correct choice is: (D) $5x^3 - 7x^2 + 15x - 75$

Would you like further details on any part of this process?

Related Questions

1. What is the result of adding $f(x)$ and $g(x)$ instead of subtracting?
2. How would $(g - f)(x)$ change if $f(x)$ had a different constant term?
3. How do you find the derivative of $(g - f)(x)$?
4. How would the answer change if the powers of $x$ were different in $f(x)$ and $g(x)$?
5. How does the subtraction of two polynomials relate to their graphs?

Tip

When subtracting polynomials, carefully distribute the negative sign across each term in the second polynomial to avoid errors.