Question

Efetue:
a) p(x) + q(x) quando p(x) = 5x^7 - 2x^6 + 3x^5 - x^4 + 6x^3 - 7x^2 + 8x - 4 e q(x) = x^6 - 4x^5 + x^4 + 2x^3 - x +5

b) p(x) - q(x) quando p(x) = 2x^5 + x^4 - 3x^3 + 4x^2 + 5x - 1 e q(x) = 3x^4 + 5x^3 - x^2 + 5x + 9

Answer 1

a) p(x) + q(x) quando p(x) = 5x^7 - 2x^6 + 3x^5 - x^4 + 6x^3 - 7x^2 + 8x - 4 e q(x) = x^6 - 4x^5 + x^4 + 2x^3 - x +5 

5x^7- 2x^6 + 3x^5 - x^4 + 6x^3- 7x^2 + 8x - 4 + x^6 - 4x^5 + x^4 + 2x^3 - x +5 

5x^7- x^6 - x^5 - 0^4 + 8x^3- 7x^2 + 7x + 1
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b) p(x) - q(x) quando p(x) = 2x^5 + x^4 - 3x^3 + 4x^2 + 5x - 1 e q(x) = 3x^4 + 5x^3 - x^2 + 5x + 9

2x^5 + x^4 - 3x^3 + 4x^2 + 5x - 1 -( 3x^4 + 5x^3 - x^2 + 5x + 9)

2x^5 + x^4 - 3x^3 + 4x^2 + 5x - 1 - 3x^4 - 5x^3 + x^2 - 5x - 9

2x^5 - 2x^4 - 8x^3 + 5x^2 + 0x - 10

Answer 2

$a)\\p(x)=5x^7-2x^6+3x^5-x^4+6x^3-7x^2+8x-4\\\\q(x)=x^6-4x^5+x^4+2x^3-x+5\\\\\\p(x)+q(x)=\ ?\\\\(5x^7-2x^6+3x^5-x^4+6x^3-7x^2+8x-4)+(x^6-4x^5+x^4+2x^3-x+5)=\\\\5x^7-2x^6+3x^5-x^4+6x^3-7x^2+8x-4+x^6-4x^5+x^4+2x^3-x+5=\\\\\boxed{p(x)+q(x)=5x^7-x^6-x^5+8x^3-7x^2+7x+1}\\\\\\b)\\p(x)=2x^5+x^4-3x^3+4x^2+5x-1\\\\q(x)=3x^4+5x^3-x^2+5x+9\\\\\\p(x)-q(x)=\ ?\\\\2x^5+x^4-3x^3+4x^2+5x-1-(3x^4+5x^3-x^2+5x+9)=\\\\2x^5+x^4-3x^3+4x^2+5x-1-3x^4-5x^3+x^2-5x-9=\\\\\boxed{p(x)-q(x)=2x^5-2x^4-8x^3+5x^2-10}$