Tìm x:
a) \(3x\left(3x-8\right)-9x^2+8=0\)
b)\(6x-15-x\left(5-2x\right)=0\)
c) \(x^3-16x=0\)
d) \(2x^2+3x-5=0\)
e) \(3x^2-x\left(3x-6\right)=36\)
f) \(\left(x+2\right)^2-\left(x-5\right)\left(x+1\right)=17\)
g) \(\left(x-4\right)^2-x\left(x+6\right)=9\)
h) \(4x\left(x-1000\right)-x+1000=0\)
i) \(x^2-36=0\)
j) \(x^2y-2+x+x^2-2y+xy=0\)
k) \(x\left(x+1\right)-\left(x-1\right).\left(2x-3\right)=0\)
l) \(3x^3-27x=0\)
Xác định a, b để \(f\left(x\right)⋮g\left(x\right)\)
a) f(x)= \(2x^3-3x^2+ax+b\) ; \(g\left(x\right)=x^2+x+2\)
b) \(f\left(x\right)=2x^4+ax^2+b\) ; \(g\left(x\right)=x^2-x-3\)
c) \(f\left(x\right)=3x^4-8x^3-10x^2+ax-b\) ; \(g\left(x\right)=3x^2-2x+1\)
d) \(f\left(x\right)=ax^3+bx^2-11x+30\) ; \(g\left(x\right)=x^2-3x-10\)
Thực hiện phép tính
a,\(\left(x-y\right)\left(y^2+y+1\right)+\left(\dfrac{1}{3}x^2y-y\right)\left(2x+y^2\right)\)
b,\(2x^2\left(x-2\right)+3x\left(x^2-x-2\right)-5\left(3-x^2\right)\)
c,\(\left(x-1\right)\left(x-3\right)-\left(4-x\right)\left(2x-1\right)-3x^3+2x-5\)
Xác định a, b để f(x) \(⋮\) g(x)
a) \(f\left(x\right)=2x^3-3x^2+ax+b\) ; \(g\left(x\right)=x^2+x+2\)
b) \(f\left(x\right)=2x^4+2x^2+b\) ; \(g\left(x\right)=x^2-x-3\)
c) \(f\left(x\right)=3x^4-8x^3-10x^2+ax-b\) ; \(g\left(x\right)=3x^2-2x+1\)
d) \(f\left(x\right)=ax^3+bx^2-11x+30\) ; \(g\left(x\right)=x^2-3x-10\)
a)làm tính nhân: (x+2)\(\left(x^2+3x+1\right)\)
b)Làm tính chia: \(\left(2x^3+10x^2+9x+4\right):\left(x+4\right)\)
Tìm x biết :
a ) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
b ) \(2x^2+7x+3\) = 0
c ) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
d ) \(2x^2+11x+9=0\)
e ) \(x\left(x+2\right)-x^2-8=0\)
f ) \(\left(x-3\right)\left(x^2+3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
Làm tính chia:
a) \(\left(-2x^4+5x^3-x^2+8\right):\left(3x^2-1\right)\)
b) \(\left(5x^4-2x^2+5\right):\left(3x^2+1\right)\)
Cho \(P\left(x\right)=x^4+3x^3-x^2+ax+b\) và \(Q\left(x\right)=x^2+2x-3\). Xác định a và b sao cho đa thức \(P\left(x\right)⋮Q\left(x\right)\)
Rút gọn các biểu thức sau :
a) \(\left(x+2\right)\left(x-2\right)-\left(x-3\right)\left(x+1\right)\)
b) \(\left(2x+1\right)^2+\left(3x-1\right)^2+2\left(2x+1\right)\left(3x-1\right)\)