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![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\)
\(\Rightarrow f\left(x\right)=x^4-x^3+3x-1\)
\(\Rightarrow g\left(x\right)=x^4+4x^3+x-5\)
\(b,\)
\(A\left(x\right)=f\left(x\right)-g\left(x\right)=x^4-x^3+3x-1-x^4-4x^3-x+5\)
\(=-5x^3-x+4\)
\(B\left(x\right)=f\left(x\right)+g\left(x\right)=x^4-x^3+3x-1+x^4+4x^3+x-5\)
\(=2x^4+3x^3+4x-6\)
\(c,\)
Thay \(x=-2\) vào \(A\left(x\right)\) , ta được :
\(A\left(x\right)=-5.\left(-2\right)^3+2+4=46\)
Thay \(x=2\) vào \(A\left(x\right)\) , ta được :
\(A\left(x\right)=-5.2^3-2+4=-38\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a) Ta có: \(P\left(x\right)=3x^4+2x^2-3x^4-2x^2+2x-5\)
\(=\left(3x^4-3x^4\right)+\left(2x^2-2x^2\right)+2x-5\)
\(=2x-5\)
Bài 1:
b)
\(P\left(-1\right)=2\cdot\left(-1\right)-5=-2-5=-7\)
\(P\left(3\right)=2\cdot3-5=6-5=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(f\left(x\right)=x^3-2x^2+3x+2\)
\(g\left(x\right)=-x^3-3x^2+2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
f(x) = x2 - x + 5
g(x) = -x2 + 2x + 3
b)
h(x) = f(x) + g(x) = x2 - x + 5 - x2 + 2x + 3
= x + 8
a: \(f\left(x\right)=2x^2+\dfrac{2}{3}x^2-\dfrac{3}{5}+1-\left(-2\dfrac{1}{3}\right)x^2-1\dfrac{2}{5}x\)
\(=\left(2x^2+\dfrac{2}{3}x^2+\dfrac{7}{3}x^2\right)-\dfrac{7}{5}x+\dfrac{2}{5}\)
\(=5x^2-1,4x+0,4\)
\(g\left(x\right)=\dfrac{1}{3}\cdot\left(3x\right)^2+2\dfrac{1}{3}x-3-\left(-1\dfrac{2}{3}\right)x-5x^2\)
\(=\dfrac{1}{3}\cdot9x^2+\dfrac{7}{3}x-3+\dfrac{5}{3}x-5x^2\)
\(=-2x^2+4x-3\)
b: h(x)=f(x)+g(x)
\(=5x^2-1,4x+0,4-2x^2+4x-3\)
\(=3x^2+2,6x-2,6\)
k(x)=g(x)-f(x)
\(=-2x^2+4x-3-5x^2+1,4x-0,4\)
\(=-7x^2+5,4x-3,4\)
c: \(h\left(2\right)=3\cdot2^2+2,6\cdot2-2,6=12+2,6=14,6\)
\(k\left(-2\right)=-7\cdot\left(-2\right)^2+5,4\cdot\left(-2\right)-3,4\)
=-28-10,8-3,4
=-28-14,2
=-42,2