Question

Add these polynomials and simplify. Enter your response in standard form. (x4 − 9x + 5x7) + (5x − 10 + 3x4 − 2x2)

Answer 1

5x7 + 4x4 - 2x2 - 4x - 10

Explanation:

To add both polynomials, there must be a rearrangement of the terms of both polynomials after removing he parenthesis. The rearrangement is such that items are group together based on the power of x. As such,

(x4 − 9x + 5x7) + (5x − 10 + 3x4 − 2x2)

= x4 − 9x + 5x7 + 5x − 10 + 3x4 − 2x2

Rearranging...

= 5x7 + x4 + 3x4 -2x2 - 9x + 5x - 10

simplifying,

= 5x7 + 4x4 - 2x2 - 4x - 10

Answer 2

Tom simplify the given expression we proceed as follows:
(x^4 − 9x + 5x^7) + (5x − 10 + 3x^4 − 2x^2)
We open the parenthesis
x^4-9x+5x^7+5x-10+3x^4-2x^2
put like terms together:
x^4+3x^4-9x+5x+5x^7-10-2x^2
simplifying the above we get:
4x^4-4x+5x^7-10-2x^2
Thus can be rewritten in order of the highest degree as:
5x^7+4x^4-2x^2-4x-10

Answer: 5x^7+4x^4-2x^2-4x-10