Let f(x) = x^3 + 3x ^2 + 4x - 7 and g(x) = -7x^4 + 5x^3 +x^2 - 7. What is the coefficient of x^3 in the sum f(x) + g(x)?
Thanks.
Since we can only add "like" terms, wouldn't we have to add
x^3 + 5x^3 ??
And that would give us ..... ?
I still don't get it. Could you explain a little more? Thanks Reiny
To find the coefficient of x^3 in the sum f(x) + g(x), we need to add the terms that have x^3 from both functions.
The term with x^3 from f(x) is 3x^3.
The term with x^3 from g(x) is 5x^3.
Adding these two terms together gives: 3x^3 + 5x^3 = 8x^3.
Therefore, the coefficient of x^3 in the sum f(x) + g(x) is 8.
To find the coefficient of x^3 in the sum f(x) + g(x), we need to add the coefficients of x^3 in the two functions f(x) and g(x).
Looking at f(x) = x^3 + 3x^2 + 4x - 7, we can see that the coefficient of x^3 is 1.
For g(x) = -7x^4 + 5x^3 + x^2 - 7, the coefficient of x^3 is 5.
To find the sum f(x) + g(x), we add the corresponding terms with the same powers of x:
f(x) + g(x) = (1x^3 + -7x^4) + (3x^2 + x^2) + (4x + -7)
Simplifying, we get:
f(x) + g(x) = -7x^4 + (1 + 3)x^3 + (1 + 4)x^2 + (4 - 7)x
= -7x^4 + 4x^3 + 5x^2 - 3x
Therefore, the coefficient of x^3 in the sum f(x) + g(x) is 4.