Question

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Answer 1

$p_1(x)=x^4-4x^2-3\\p_2(x)=-3x^4-5x^2-3\\\\p_1(x)+p_2(x)=x^4-4x^2-3+(-3x^4-5x^2-3)=\\=x^4-4x^2-3-3x^4-5x^2-3=-2x^4-9x^2-6\\\\\ p_1(x)-p_2(x)=x^4-4x^2-3-(-3x^4-5x^2-3)=\\=x^4-4x^2-3+3x^4+5x^2+3=4x^4+x^2$