Which polynomial represents the sum: $(8 x^{2} + 5 x + 3) + (- 5 x^{6} = 2 x^{5} - 4 x^{2} - 2 x)$ $(8x^2+5x+3)+(-5x^6=2x^5-4x^2-2x)$ ?

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Answer 1 · 2016-12-26T23:40:16

I take it the $=$ $=$ in the second parts was meant as a $+$ $+$ (forgot the shift-button?)

First we lose the brackets (no sign change because of the $+$ $+$ between them), then we order by power:

$= - 5 x^{6} + 2 x^{5} + 8 x^{2} - 4 x^{2} + 5 x - 2 x + 3$ $=-5x^6+2x^5+8x^2-4x^2+5x-2x+3$

We may add like powers:

$= - 5 x^{6} + 2 x^{5} + (8 - 4) x^{2} + (5 - 2) x + 3$ $=-5x^6+2x^5+(8-4)x^2+(5-2)x+3$

$= - 5 x^{6} + 2 x^{5} + 4 x^{2} + 3 x + 3$ $=-5x^6+2x^5+4x^2+3x+3$

Which polynomial represents the sum: (8x2+5x+3)+(−5x6=2x5−4x2−2x)(8x^2+5x+3)+(-5x^6=2x^5-4x^2-2x)?