f(x)=11x^3+3x^2-4x+2 and g(x)=5x^3-7x+2. What is f(x) - g(x)? Show all of your steps and write your final answer in factored form.
subtract the matching terms
(11x^3 - 5x^3) + 3x^2 + (-4x - 7x) + (2 + 2) = 6x^3 + 3x^2 - 11x = x(6x^2 + 3x - 11)
Complete each item below by finding the missing factor. Virite your answer on the space provided.
1.7?- 16 = (x +4)
2.3+4x² - 9 = (x+3)(- (-
3.3.2 + 4x2 + 11x - 10 = (3x - 2)
4. 4x3 + 11x2 - 11x + 2 = (4x - 1)(
5. 5x3 + 10.x2 + x + 2 = (x + 2)(
x+2
To find f(x) - g(x), we need to subtract the two functions.
f(x) - g(x) = (11x^3 + 3x^2 - 4x + 2) - (5x^3 - 7x + 2)
Step 1: Distribute the negative sign to every term in g(x):
f(x) - g(x) = 11x^3 + 3x^2 - 4x + 2 - 5x^3 + 7x - 2
Step 2: Group like terms together:
f(x) - g(x) = (11x^3 - 5x^3) + (3x^2) + (-4x + 7x) + (2 - 2)
Step 3: Combine like terms:
f(x) - g(x) = 6x^3 + 3x^2 + 3x + 0
Now, let's factor our final answer:
f(x) - g(x) = 3x(2x^2 + x + 1)
So, f(x) - g(x) in factored form is 3x(2x^2 + x + 1).
To find f(x) - g(x), we need to subtract the expression for g(x) from the expression for f(x).
f(x) - g(x) = (11x^3 + 3x^2 - 4x + 2) - (5x^3 - 7x + 2)
Step 1: Distribute the negative sign to each term in g(x):
f(x) - g(x) = 11x^3 + 3x^2 - 4x + 2 - 5x^3 + 7x - 2
Step 2: Combine like terms:
f(x) - g(x) = (11x^3 - 5x^3) + (3x^2) + (-4x + 7x) + (2 - 2)
Simplify further:
f(x) - g(x) = 6x^3 + 3x^2 + 3x + 0
Step 3: Factor out common terms if possible:
f(x) - g(x) = 3x(2x^2 + x + 1)
So, f(x) - g(x) in factored form is 3x(2x^2 + x + 1).