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Bài làm:
a) \(x^2-6x+4=\left(x^2-6x+9\right)-5=\left(x-3\right)^2-\left(\sqrt{5}\right)^2\)
\(=\left(x-3-\sqrt{5}\right)\left(x-3+\sqrt{5}\right)\)
b) \(x^2-4x+3=x^2-x-3x+3=\left(x-1\right)\left(x-3\right)\)
c) \(6x^2-5x+1=6x^2-3x-2x+1=\left(2x-1\right)\left(3x-1\right)\)
d) \(3x^2+13x-10=3x^2+15x-2x-10=\left(x-5\right)\left(3x-2\right)\)
\(x^3-x^2-14x+24\)
\(=x^3-2x^2+x^2-2x-12x+24\)
\(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-2\right).\left[x^2+4x-3x-12\right]\)
\(=\left(x-2\right).\left[x\left(x+4\right)-3\left(x+4\right)\right]\)
\(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)
\(x^4+x^3+2x-4\)
\(=x^4-x^3+2x^3-2x^2+2x^2-2x+4x-4\)
\(=x^3\left(x-1\right)+2x^2\left(x-1\right)+2x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+2x^2+2x+4\right)\)
\(=\left(x-1\right).\left[x^2\left(x+2\right)+2\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+2\right)\)
\(8x^4-2x^3-3x^2-2x-1\)
\(=8x^4-8x^3+6x^3-6x^2+3x^2-3x+x-1\)
\(=8x^3\left(x-1\right)+6x^2\left(x-1\right)+3x\left(x-1\right)+x-1\)
\(=\left(x-1\right)\left(8x^3+6x^2+3x+1\right)\)
\(=\left(x-1\right)\left[\left(8x^3+1\right)+\left(6x^2+3x\right)\right]\)
\(=\left(x-1\right)\left[\left(2x+1\right)\left(4x^2-2x+1\right)+3x\left(2x+1\right)\right]\)
\(=\left(x-1\right)\left(2x+1\right)\left(4x^2+x+1\right)\)
\(3x^2-7x+2\)
\(=3x^2-6x-x+2\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
Chúc bạn học tốt.
Bài làm
a) 3x2 - 6x2 + 3x
= -3x2 + 3x
= 3x( 1 - x )
b) 3x2 + 5x - 3xy - 5y
= ( 3x2 - 3xy ) + ( 5x - 5y )
= 3x( x - y ) + 5( x - y )
= ( x - y )( 3x + 5 )
c) x3 + 2x2 + x
= x( x2 + 2x + 1 )
= x( x2 + 2.x.1 + 12 )
= x( x + 1 )2
d) xy + y2 - x - y
= ( xy - x ) + ( y2 - y )
= x( y - 1 ) + y( y - 1 )
= ( y - 1 )( x + y )
# Học tốt #
a) = (x + 1)^3 - 27z^3 = (x+1 - 3z)( (x+1)^2 + 3z(x+1) + 9z^2 )
b)= x^2 + x+ 3x + 3 = x (x+1) +3 (x+1) =(x+3)(x+1)
c) = 2x^2 - 2x + 5x - 5 = 2x(x-1) + 5(x-1) = (2x+5)(x-1)
d) = (a^2 + 1 - 2a)(a^2 +2a +1) = (a-1)^2 * (a+1)^2
e) = x^3 ( x-1) - (x^2 - 1) = x^3 ( x-1) - (x+1)(x-1) = (x^3 -x -1)(x-1)
a) \(6x^2+6\)
\(=6\left(x^2+1\right)\)
b) \(2x^2-18\)
\(=2\left(x^2-9\right)\)
\(=2\left(x-3\right)\left(x+3\right)\)
c) \(3x^2-3xy+4x-4y\)
\(=\left(3x^2-3xy\right)+\left(4x-4y\right)\)
\(=3x\left(x-y\right)+4\left(x-y\right)\)
\(=\left(3x-4\right)\left(x-y\right)\)
a) \(\left(x^3-9x^2+27x-27\right)\)\(:\)\(\left(x-3\right)\)
\(=\left(x-3\right)^3\)\(:\)\(\left(x-3\right)\)
\(=\left(x-3\right)^2\)
c) \(\frac{x^2-4}{2x}:\frac{3x-6}{6}\)
\(=\frac{\left(x-2\right)\left(x+2\right)}{2x}.\frac{6}{3\left(x-2\right)}\)
\(=\frac{\left(x+2\right)}{x}\)
a) (x2-4x+3)(x2-10x+24)+8=((x2-x)-(3x-3))((x2-6x)-(4x-24))+8
=(x(x-1)-3(x-1))(x(x-6)-4(x-6))+8=(x-1)(x-3)(x-4)(x-6)+8=((x-1)(x-6))(x-3)(x-4))+8
=(x2-7x+6)(x2-7x+12)+8
Đặt x2-7x+6=a
Ta có : a(a+6)+8=a2+6a+8=(a+2)(a+4)=(x2-7x+8)(x2-7x+10)=(x2-7x+8)(x-5)(x-2)
b) Tương tự như câu a kết quả là (x-3)(x3+9x2+21x+9)
c) x4+x3+6x2+3x+9=(x4+x3+3x2)+(3x2+3x+9)=x2(x2+x+3)+3(x2+x+3)=(x2+x+3)(x2+2)
A/ \(16x-5x^2-3=\left(15x-3\right)-\left(5x^2-x\right)=3\left(5x-1\right)-x\left(5x-1\right)=\left(5x-1\right)\left(3-x\right)\)
B/ \(x^3-3x^2+1-3x=\left(x^3-4x^2+x\right)+\left(x^2-4x+1\right)=x\left(x^2-4x+1\right)+\left(x^2-4x+1\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
C/ \(x^3-3x^2-4x+12=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
D/ \(\left(2x+1\right)^2-\left(x-1\right)^2=\left(2x+1-x+1\right)\left(2x+1+x-1\right)=3x\left(x+2\right)\)
\(a,x^2+2x-3\)
\(=x^2+2x+1-4\)
\(=\left(x+1\right)^2-2^2\)
\(=\left(x+3\right)\left(x-1\right)\)
\(b,x^2-3x-10\)
\(=x^2+2x-5x-10\)
\(=x\left(x+2\right)-5\left(x+2\right)\)
\(=\left(x-5\right)\left(x+2\right)\)
\(c,x^2-13x+36\)
\(=x^2-4x-9x+36\)
\(=x\left(x-4\right)-9\left(x-4\right)\)
\(=\left(x-9\right)\left(x-4\right)\)
\(d,x^2+3x-18\)
\(=x^2+6x-3x-18\)
\(=x\left(x+6\right)-3\left(x+6\right)\)
\(=\left(x-3\right)\left(x+6\right)\)