What is the standard form of a polynomial #(-5x^4 + 3x^3 - 3x^2 - 6x) + (3x^4 + 7x^3 + 4x^2 - 9x + 4)#?

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Answer 1 · 2017-12-12T12:55:12

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^3 - 3x^2 - 6x + 3x^4 + 7x^3 + 4x^2 - 9x + 4#

Next, group like terms in descending order of their exponents:

#-5x^4 + 3x^4 + 3x^3 + 7x^3 - 3x^2 + 4x^2 - 6x - 9x + 4#

Now, combine like terms:

#(-5 + 3)x^4 + (3 + 7)x^3 + (-3 + 4)x^2 + (-6 - 9)x + 4#

#-2x^4 + 10x^3 + 1x^2 + (-15)x + 4#

#-2x^4 + 10x^3 + x^2 - 15x + 4#