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![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a) \(-5\left(x^2-3x+1\right)+x\left(1+5x\right)=x-2\)
\(\Rightarrow-5x^2+15x-5+x+5x^2=x-2\)
\(\Rightarrow16x-5=x-2\)
\(\Rightarrow16x-x=5-2\)
\(\Rightarrow15x=3\)
\(\Rightarrow x=\dfrac{15}{3}=5\)
b) \(12x^2-4x\left(3x+5\right)=10x-17\)
\(\Rightarrow12x^2-12x^2-20x=10x-17\)
\(\Rightarrow-20x=10x-17\)
\(\Rightarrow-20x-10x=-17\)
\(\Rightarrow-30x=-17\)
\(\Rightarrow x=\dfrac{-30}{-17}=\dfrac{30}{17}\)
c) \(-4x\left(x-5\right)+7x\left(x-4\right)-3x^2=12\)
\(\Rightarrow-4x^2+20x+7x^2-28x-3x^2=12\)
\(\Rightarrow-8x=12\)
\(\Rightarrow x=\dfrac{12}{-8}=-\dfrac{4}{3}\)
Bài 2:
a) \(\left(x+5\right)\left(x-7\right)-7x\left(x-3\right)\)
\(=x^2-7x+5x-35-7x^2+21x\)
\(=-6x^2+19x-35\)
b) \(x\left(x^2-x-2\right)-\left(x-5\right)\left(x+1\right)\)
\(=x^3-x^2-2x-x^2+x-5x-5\)
\(=x^3-2x^2-6x-5\)
c) \(\left(x-5\right)\left(x-7\right)-\left(x+4\right)\left(x-3\right)\)
\(=x^2-7x-5x+35-x^2-3x+4x-12\)
\(=11x+23\)
d) \(\left(x-1\right)\left(x-2\right)-\left(x+5\right)\left(x+2\right)\)
\(=x^2-2x-x+2-x^2+2x+5x+10\)
\(=4x+12\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,-3x^2+7x-9+\left(x-1\right)\left(x+2\right)\\ =-3x^2+7x-9+x^2-x+2x-2\\ =\left(-3x^2+x^2\right)+\left(7x-x+2x\right)-\left(9+2\right)\\ =-2x^2+8x-11\\ b,x\left(x-5\right)-2x\left(x+1\right)\\ =x^2-5x-2x^2-2x\\ =\left(x^2-2x^2\right)-\left(5x+2x\right)\\ =-3x^2-7x\\ c,4x\left(x^2-x+1\right)-\left(x-1\right)\left(x^2-x\right)\\ =4x^3-4x^2+4x-x\left(x^2-x\right)+x^2-x\\ =4x^3-4x^2+4x-x^3+x^2+x^2-x\\ =\left(4x^3-x^3\right)+\left(-4x^2+x^2+x^2\right)+\left(4x-x\right)\\ =3x^3-2x^2+3x\\ =x\left(3x^2-2x+3\right)\)
\(d,-5x\left(x-5\right)+\left(x-3\right)\left(x^2-7\right)\\ =-5x^2+25x+x\left(x^2-7\right)-3\left(x^2-7\right)\\ =-5x^2+25x+x^3-7x-3x^2+21\\ =\left(-5x^2-3x^2\right)+\left(25x-7x\right)+x^3+21\\ =-8x^2+x^3+18x+21\)
![](https://rs.olm.vn/images/avt/0.png?1311)
26:
A=12x^2+10x-6x-5-(12x^2-8x+3x-2)
=12x^2+4x-5-12x^2+5x+2
=9x-3
Khi x=-2 thì A=-18-3=-21
25:
b: \(\left(y-3\right)\left(y^2+y+1\right)-y\left(y^2-2\right)\)
=y^3+y^2+y-3y^2-3y-3-y^3+2y
=-2y^2-3
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(M\left(x\right)=-2x^5+5x^2+7x^4-5x+8+2x^5-7x^4-4x^2+6\)
\(=\left(-2x^5+2x^5\right)+\left(7x^4-7x^4\right)+\left(5x^2-4x^2\right)-9x+\left(8+6\right)\)
\(=x^2-9x+14\)
\(N\left(x\right)=7x^7+x^6-5x^3+2x^2-7x^7+5x^3+3\)
\(=\left(7x^7-7x^7\right)+x^6-\left(5x^3-5x^3\right)+2x^2+3\)
\(=x^6+2x^2+3\)
b) Đa thức M(x) có hệ số cao nhất là 1
hệ số tự do là 14
bậc 2
Đa thức N(x) có hệ số cao nhất là 1
hệ số tự do là 3
bậc 6
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A\left(x\right)=-1+5^6-6x^2-5-9x^6+4x^4-3x^2\)
\(=-9x^6+4x^4-\left(3x^2+6x^2\right)+\left(5^6-1-5\right)\)
\(=-9x^6+4x^4-9x^2+\left(5^6-1-5\right)-15619\)
\(B\left(x\right)=2-5x^2+3x^4-4x^2+3x+x^4-4x^6-7x\)
\(=-4x^6+\left(3x^4+x^4\right)-\left(5x^2+4x^2\right)+\left(3x-7x\right)+2\)
\(=-4x^6+4x^4-9x^2-4x+2\)
\(A\left(x\right)-B\left(x\right)\)
\(=\left(-9x^6+4x^4-9x^2-15619\right)-\left(-4x^6+4x^4-9x^2-4x+2\right)\)
\(=-9x^6+4x^4-9x^2-15619+4x^6-4x^4+9x^2+4x-2\)
\(=-5x^6+4x-15621\)
Hình như C(x) vô nghiệm
a: Trường hợp 1: x<-3
A=5(-x-3)-7x+4=-5x-15-7x+4=-12x-11
Trường hợp 2: x>=-3
A=5(x+3)-7x+4=5x+15-7x+4=-2x+19
b: Trường hợp 1: x<-1
B=2(-x-1)-4x-5=-2x-2-4x-5=-6x-7
Trường hợp 2: x>=-1
B=2(x+1)-4x-5=2x+2-4x-5=-2x-3
c: Trường hợp 1: x<2
C=9x-6+2-x=8x-4
Trường hợp 2: x>=2
C=9x-6+x-2=10x-8