Please help ASAPPP!!!!
I have no idea how to even start on this!
f(x)=9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4. What is f(x)-g(x)? Show all of your steps and wrote your final answer in factored form.
If someone could help me work through this problem that would be great!
for heavens sake it says to subtract, so subtract
9-5 = 4
2 - 0 = 2
-5 - -7 = 2
4-4 = 0
so
4 x^3 + 2 x^2 + 2 x
2x(2x^2 + x + 1)
To find the expression for f(x) - g(x), you need to subtract g(x) from f(x) term by term. Here are the steps:
1. Start with the expression for f(x): f(x) = 9x^3 + 2x^2 - 5x + 4.
2. Now, subtract g(x) from f(x) term by term:
f(x) - g(x) = (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4).
3. Distribute the negative sign to all terms in g(x):
f(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4.
4. Combine like terms: Add or subtract the coefficients of terms with the same exponent.
f(x) - g(x) = (9x^3 - 5x^3) + (2x^2) + (-5x + 7x) + (4 - 4).
Simplifying further:
f(x) - g(x) = 4x^3 + 2x^2 + 2x.
5. Finally, the expression f(x) - g(x), written in factored form, is:
f(x) - g(x) = 2x(2x^2 + x + 1)(x + 1).
Therefore, the final answer, in factored form, is 2x(2x^2 + x + 1)(x + 1).
Of course, I'd be happy to help you with this problem! To find f(x) - g(x), we need to subtract the two functions term by term.
First, let's write down f(x) and g(x):
f(x) = 9x^3 + 2x^2 - 5x + 4
g(x) = 5x^3 - 7x + 4
Now, to find f(x) - g(x), we subtract the corresponding terms of the two functions:
(f(x) - g(x)) = (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
To simplify this expression, we distribute the negative sign to all the terms in g(x):
(f(x) - g(x)) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
Next, we can combine like terms:
(f(x) - g(x)) = (9x^3 - 5x^3) + (2x^2) + (-5x + 7x) + (4 - 4)
Simplifying further:
(f(x) - g(x)) = 4x^3 + 2x^2 + 2x
Now, we need to factor the equation. Factoring involves finding common factors and grouping terms.
To factor out a common factor from the equation, we look for the highest power of x that is common to all the terms. In this case, the highest power of x that is common to all terms is x.
So, we can factor out x from the equation:
(f(x) - g(x)) = x(4x^2 + 2x + 2)
Therefore, the factored form of f(x) - g(x) is x(4x^2 + 2x + 2).
I hope this explanation helps you understand how to solve this problem! Let me know if you have any further questions.