Tính f(x) + g(x), f(x) – g(x), g(x) – f(x) f(x)= x mũ 5 – 2x mũ 2 + 7x mũ 4 – 8x mũ 3 + 2x mũ 2- 1/4x + 3x mũ 2 g(x)= 5x mũ 4 – x mũ 5 + x mũ 2- 2

Đáp án:f(x)+g(x)$=8x^{4}-\frac{26}{3}x^{3}+7x^{2}-\frac{1}{4}x+\frac{1}{4}$

f(x)-g(x)$=2x^{5}+2x^{4}-\frac{22}{3}x^{3}-x^{2}-\frac{1}{4}x-\frac{1}{4}$

g(x)-f(x)$=-2x^{5}-2x^{4}+\frac{22}{3}x^{3}+x^{2}+\frac{1}{4}x+\frac{1}{4}$

Giải thích các bước giải:

 $f(x)=x^{5}+7x^{4}-8x^{3}+3x^{2}-\frac{1}{4}x$

$g(x)=-x^{5}+5x^{4}-\frac{2}{3}x^{3}+4x^{2}+\frac{1}{4}$

$* f(x)+g(x)=x^{5}+7x^{4}-8x^{3}+3x^{2}-\frac{1}{4}x-x^{5}+5x^{4}-\frac{2}{3}x^{3}+4x^{2}+\frac{1}{4}$

$=(x^{5}-x^{5})+(7x^{4}+x^{4})-(8x^{3}+\frac{2}{3}x^{3})+(3x^{2}+4x^{2})-\frac{1}{4}x+\frac{1}{4}$

$=8x^{4}-\frac{26}{3}x^{3}+7x^{2}-\frac{1}{4}x+\frac{1}{4}$

$*f(x)-g(x)=x^{5}+7x^{4}-8x^{3}+3x^{2}-\frac{1}{4}x-(-x^{5}+5x^{4}-\frac{2}{3}x^{3}+4x^{2}+\frac{1}{4})$

$=x^{5}+7x^{4}-8x^{3}+3x^{2}-\frac{1}{4}x+x^{5}-5x^{4}+\frac{2}{3}x^{3}-4x^{2}-\frac{1}{4}$

$=(x^{5}+x^{5})+(7x^{4}-5x^{4})-(8x^{3}-\frac{2}{3}x^{3})+(3x^{2}-4x^{2})-\frac{1}{4}x-\frac{1}{4}$

$=2x^{5}+2x^{4}-\frac{22}{3}x^{3}-x^{2}-\frac{1}{4}x-\frac{1}{4}$

$* g(x)-f(x)=-x^{5}+5x^{4}-\frac{2}{3}x^{3}+4x^{2}+\frac{1}{4}-(x^{5}+7x^{4}-8x^{3}+3x^{2}-\frac{1}{4}x)$

$=-x^{5}+5x^{4}-\frac{2}{3}x^{3}+4x^{2}+\frac{1}{4}-x^{5}-7x^{4}+8x^{3}-3x^{2}+\frac{1}{4}x$

$=(-x^{5}-x^{5})+(5x^{4}-7x^{4})-(\frac{2}{3}x^{3}-8x^{3})+(4x^{2}-3x^{2})+\frac{1}{4}x+\frac{1}{4}$

$=-2x^{5}-2x^{4}+\frac{22}{3}x^{3}+x^{2}+\frac{1}{4}x+\frac{1}{4}$