Use the addition problem (3x2+4x4−4x+x5)+(2x−5x2+4x4+2x5) to answer the question.
Which expression correctly rewrites the polynomials to help in combining like terms?
-4x + 3x^2 + 0 x^3 + 4 x^4 + x^5
2 x - 5 x^2 + 0 x^3 + 4 x^4 +2x^5
---------------------------------------------------- add
-2x - 2x^2 + 8 x^4 etc etc etc
To rewrite the given polynomials to help in combining like terms, we need to rearrange the terms of each polynomial so that terms with the same variable and exponent are grouped together.
Given expression: (3x^2 + 4x^4 - 4x + x^5) + (2x - 5x^2 + 4x^4 + 2x^5)
To rearrange the terms, we can rewrite the expression in descending order of the variable exponents:
x^5 + 4x^4 + 3x^2 - 4x + 2x^5 + 2x - 5x^2 + 4x^4
Now, let's combine the like terms:
(x^5 + 2x^5) + (4x^4 + 4x^4) + (3x^2 - 5x^2) + (-4x + 2x)
Simplifying further, we have:
3x^5 + 8x^4 - 2x^2 - 2x
So, the correct expression that rewrites the polynomials to help in combining like terms is:
3x^5 + 8x^4 - 2x^2 - 2x