f (x) = 9x^3 + 2x^2 - 5x + 4 and g(x) = 5x^3 - 7x + 4. What is f (x) - g(x)? Show all your stes and write your final answer in factored form.
I am really stumped on this, could someone help me?
just subtract, term by term
4 x^3
2 x^2
2 x
0
4x^3 + 2 x^2 + 2 x
2 x (2 x^2 + x + 1)
Is that the answer? 2 x (2 x^2 + x + 1)? Or do I need to factor it, like it says?
So how do I write it in step by step form, for an essay?
Of course! Let's go through the steps to find f(x) - g(x) and write the final answer in factored form.
Step 1: Start with the given functions:
f(x) = 9x^3 + 2x^2 - 5x + 4
g(x) = 5x^3 - 7x + 4
Step 2: Subtract g(x) from f(x):
f(x) - g(x) = (9x^3 + 2x^2 - 5x + 4) - (5x^3 - 7x + 4)
Step 3: Distribute the subtraction across both terms inside the brackets:
f(x) - g(x) = 9x^3 + 2x^2 - 5x + 4 - 5x^3 + 7x - 4
Step 4: Combine like terms by grouping their coefficients:
f(x) - g(x) = (9x^3 - 5x^3) + (2x^2) + (-5x + 7x) + (4 - 4)
Step 5: Simplify:
f(x) - g(x) = 4x^3 + 2x^2 + 2x
Now, to write the final answer in factored form, we can factor out the common factor, which is 2x:
f(x) - g(x) = 2x(2x^2 + x + 1)
Therefore, the final answer in factored form is 2x(2x^2 + x + 1).