Which polynomial represents the sum: #(5x^4-3x^2-2x)+(2x^4+2x^3+2x^2+x+1)#?

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Answer 1 · 2017-08-23T22:13:59

See a solution process below:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

#5x^4 - 3x^2 - 2x + 2x^4 + 2x^3 + 2x^2 + x + 1#

Next, group like terms:

#5x^4 + 2x^4 + 2x^3 - 3x^2 + 2x^2 - 2x + x + 1#

Now, combine like terms:

#5x^4 + 2x^4 + 2x^3 - 3x^2 + 2x^2 - 2x + 1x + 1#

#(5 + 2)x^4 + 2x^3 + (-3 + 2)x^2 + (-2 + 1)x + 1#

#7x^4 + 2x^3 + (-1)x^2 + (-1)x + 1#

#7x^4 + 2x^3 - 1x^2 - 1x + 1#

#7x^4 + 2x^3 - x^2 - x + 1#