a)f(x)+g(x)=\(x^5-4x^4-2x^2-7-2x^5+6x^4-2x^2+6.\)

=\(-x^5+2x^4-4x^2-1\)

f(x)-g(x)=\(x^5-4x^4-2x^2-7+2x^5-6x^4+2x^2-6\)

=\(3x^5-10x^4-13\)

b)f(x)+g(x)=\(5x^4+7x^3-6x^2+3x-7-4x^4+2x^3-5x^2+4x+5\)

=\(x^4+9x^3-11x^2+7x-2\)

f(x)-g(x)=\(5x^4+7x^3-6x^2+3x-7+4x^4-2x^3+5x^2-4x-5\)

=\(9x^4+5x^3-x^2-x-12\)

a ) 

\(f\left(x\right)+g\left(x\right)=x^5-4x^4-2x^2-7+-2x^5+6x^4-2x^2+6\)

\(\Rightarrow f\left(x\right)+g\left(x\right)=\left(x^5-2x^5\right)+\left(6x^4-4x^4\right)-\left(2x^2+2x^2\right)+\left(6-7\right)\)

\(\Rightarrow f\left(x\right)+g\left(x\right)=-x^5+2x^4-4x^2-1\)

\(f\left(x\right)-g\left(x\right)=x^5-4x^4-2x^2-7-\left(-2x^5+6x^4-2x^2+6\right)\)

\(\Rightarrow f\left(x\right)-g\left(x\right)=x^5-4x^4-2x^2-7+2x^5-6x^4+2x^2-6\)

\(\Rightarrow f\left(x\right)-g\left(x\right)=\left(x^5+2x^5\right)-\left(4x^4+6x^4\right)+\left(2x^2-2x^2\right)-\left(6+7\right)\)

\(\Rightarrow f\left(x\right)-g\left(x\right)=3x^5-10x^4-13\)

b ) Làm tương tự 

Bài 1:

Để \(F\left(x\right)=G\left(x\right)\) thì \(3x^2-8x+4=3x+4\)

\(\Leftrightarrow3x^2-11x=0\)

\(\Leftrightarrow x\left(3x-11\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{11}{3}\end{matrix}\right.\)

`1,`

`f(x)+g(x)=(5+4-2+7)+(4x^4-2x^3+3x^2+4x-1)`

`= 5+4-2+7+4x^4-2x^3+3x^2+4x-1`

`=(5x^4+4x^4)-2x^3+(4x^2+4x^2)+(-2x+4x)+(7-1)`

`= 9x^4-2x^3+8x^2+2x+6`

Đề phải là `f(x)-g(x)` chứ nhỉ :v?

`f(x)-g(x)=(5+4-2+7)-(4x^4-2x^3+3x^2+4x-1)`

`= 5+4-2+7-4x^4+2x^3-3x^2-4x+1`

`= (5x^4-4x^4)+2x^3+(-2x-4x)+(4x^2-3x^2)+(7+1)`

`= x^4+2x^3-6x+x^2+8`

`2,`

`a, (x+3)(x-1)`

`= x(x-1)+3(x-1)`

`= x*x+x*(-1)+3*x+3*(-1)`

`=x^2-x+3x-3`

`= x^2+2x-3`

`b, (4x+3)(x-2)`

`= 4x(x-2)+3(x-2)`

`= 4x*x+4x*(-2)+3*x+3*(-2)`

`= 4x^2-8x+3x-6`

`c, (2x+3)(x+1)`

`= 2x(x+1)+3(x+1)`

`= 2x*x+2x*1+3*x+3*1`

`= 2x^2+2x+3x+3`

`= 2x^2+5x+3`

`d, (5x-2)(x^2-3x+1)`

`= 5x(x^2-3x+1)+(-2)(x^2-3x+1)`

`= 5x*x^2+5x*(-3x)+5x*1+(-2)*x^2+(-2)*(-3x)+(-2)*1`

`= 5x^3-15x^2+5x-2x^2+6x-2`

`= 5x^3-17x^2+11x-2`

a. f(x)+g(x)=2x⁵−4x⁴+3x³−x²+5x−1+

2x⁵−4x⁴+3x³−x²+5x−1+

−x⁵+2x⁴−3x³−x²−2x+7+x⁵−2x⁴−2x²−x−3

=-x⁵+x⁵+2x⁴-2x⁴-3x³-x²-2x²-2x-x+7-3

=-3x³-3x²-3x+4

d. f(x)-g(x)=2x⁵−4x⁴+3x³−x²+5x−1-(−x⁵+2x⁴−3x³−x²−2x+7)

=2x⁵−4x⁴+3x³−x²+5x−1-x⁵-2x⁴+3x³+x²+2x-7

=2x⁵-x⁵-4x⁴-2x⁴+3x³+3x³-x²+x²+5x+2x-1-7

=x⁵-6x⁴+6x³+7x-8

e. f(x)-h(x)=2x⁵−4x⁴+3x³−x²+5x−1-(x⁵−2x⁴−2x²−x−3)

=2x⁵−4x⁴+3x³−x²+5x−1-x⁵+2x⁴+2x²+x+3

=2x⁵-x⁵-4x⁴+2x⁴+3x³-x²+2x²+5x+x-1+3

=x⁵-2x⁴+3x³+x²+6x-4

h. g(x)-h(x)=−x⁵+2x⁴−3x³−x²−2x+7-(x⁵−2x⁴−2x²−x−3)

=−x⁵+2x⁴−3x³−x²−2x+7-x⁵+2x⁴+2x²+x+3

=-x⁵-x⁵+2x⁴+2x⁴-3x³-x²+2x²-2x+x+7+3

=-2x⁵+4x⁴-3x³+x²-x+10

f. f(x)+g(x)+h(x)=2x⁵−4x⁴+3x³−x²+5x−1+x⁵−2x⁴−2x²−x−3

=2x⁵-x⁵+x⁵-4x⁴+2x⁴-2x⁴+3x³-3x³-x²-x²-2x²+5x-2x-x-1+7-3

=2x⁵-4x⁴-4x²+2x+3

g. f(x)+g(x)-h(x)=2x⁵−4x⁴+3x³−x²+5x−1+x⁵−2x⁴−2x²−x−3)

=2x⁵−4x⁴+3x³−x²+5x−1+x⁵+2x⁴+2x²+x+3

=2x⁵-x⁵-x⁵-4x⁴+2x⁴+2x⁴+3x³-3x³-x²-x²+2x²+5x-2x+x-1+7+3

=4x+9

n. f(x)-g(x)+h(x)=2x⁵−4x⁴+3x³−x²+5x−1-x⁵−2x⁴−2x²−x−3

=2x⁵−4x⁴+3x³−x²+5x−1-x⁵−2x⁴−2x²−x−3

=2x⁵-x⁵+x⁵-4x⁴-2x⁴-2x⁴+3x³+3x³-x²+x²-2x²+5x+2x-x-1-7-3

=2x⁵-8x⁴+6x³-2x²+6x-11

m. f(x)-g(x)-h(x)=2x⁵−4x⁴+3x³−x²+5x−1-x⁵−2x⁴−2x²−x−3)

=2x⁵−4x⁴+3x³−x²+5x−1-x⁵+2x⁴+2x²+x+3

=2x⁵-x⁵-x⁵-4x⁴-2x⁴+2x⁴+3x³+3x³-x²+x²+2x²+5x+2x+x-1-7+3

=-4x⁴+6x³+2x²+8x-5

Tham khảo:

Xét [\(f\left(x\right)+g\left(x\right)\)]+[\(f\left(x\right)-g\left(x\right)\)]=\(\left[2x^4+5x^2-3x\right]\)+\(\left[x^4-x^2+2x\right]\)

\(2f\left(x\right)=2x^4+5x^2-3x+x^4-x^2+2x\)

\(2f\left(x\right)=3x^4+4x^2-x\)

\(\Rightarrow f\left(x\right)=\dfrac{3x^4+4x^2-x}{2}\)

\(\Rightarrow f\left(x\right)=\dfrac{3}{2}x^4+2x^2-\dfrac{1}{2}x\)

Xét \(\left[f\left(x\right)+g\left(x\right)\right]-\left[f\left(x\right)-g\left(x\right)\right]=\)\(\left[2x^4+5x^2-3x\right]\)\(-\)\(\left[x^4-x^2+2x\right]\)

\(2g\left(x\right)=\)\(2x^4+5x^2-3x-x^4+x^2-2x\)

\(2g\left(x\right)=x^4+6x^2-5x\)

\(\Rightarrow g\left(x\right)=\dfrac{x^4+6x^2-5x}{2}\)

\(\Rightarrow g\left(x\right)=\dfrac{1}{2}x^4+3x^2-\dfrac{5}{2}x\)

Áp dụng quy tắc tổng hiệu đó

\(f\left(x\right)=\dfrac{\left(x^3+6x^2+3x^4\right)+\left(2x^3-x^2+3x^4\right)}{2}\)

Vậy \(f\left(x\right)=\dfrac{6x^4+3x^3+5x^2}{2}=3x^4+1,5x^3+2,5x^2\)

\(g\left(x\right)=\left(x^3+6x^2+3x^4\right)-f\left(x\right)\)

\(=\left(x^3+6x^2+3x^4\right)-\left(3x^4+1,5x^3+2,5x^2\right)\)

\(=x^3+6x^2+3x^4-3x^4-1,5x^3-2,5x^2\)

\(=\left(3x^4-3x^4\right)+\left(x^3-1,5x^3\right)+\left(6x^2-2,5x^2\right)\)

Vậy \(g\left(x\right)=-0,5x^3+3,5x^2\)