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Nham nghiem thi ta thay pt co 1 ngiem x=2/3
=> tach nhu sau :
\(3x^3-2x^2-3x^2+2x+3x-2\)
\(3x^2\left(x-\frac{2}{3}\right)-3x\left(x-\frac{2}{3}\right)+3\left(x-\frac{2}{3}\right)\)
\(\left(x-\frac{2}{3}\right)\left(3x^2-3x+3\right)\)
Chuc ban hoc tot
Ta có :
a ) \(a^5+a^4+a^3+a^2+a+1=\left(a+1\right)\left(a^2-a+1\right)\left(a^2+a+1\right)\)
b ) \(x^{10}+x^5+1=\left(x^2+x+1\right)\left(x^8-x^7+x^5-x^4+x^3-x+1\right)\)
Vì ko có thời gian nên mình làm tắt luôn nha !!!!
1.a) (3x+1)2-4(x-2)2= (3x+1)2-[2(x-2)]2=[(3x+1)-2(x-2)][(3x+1)+2(x-2)]=(x+3)(5x-1)
b) (a2+b2-5)2-4(ab+2)2= (a2+b2-5)2-[2(ab+2)]2 = (a2+b2-5-2ab-4)(a2+b2-5+2ab+4)=[(a-b)2-9][(a+b)2-1]
2. 3x2+9x-30=3x2-6x+15x-30=3x(x-2)+15(x-2)=3(x+5)(x-2)
b. x3-5x2-14x=x3+2x2-7x2-14x=x2(x+2)-7x(x+2)=(x2-7x)(x+2)
a) \(\left(3x+1\right)^2-4\left(x-2\right)^2\)
\(=\left(3x+1\right)^2-\left[2.\left(x-2\right)\right]^2\)
\(=\left(3x+1\right)^2-\left(2x-4\right)^2\)
\(=\left[3x+1-2x+4\right].\left[3x+1+2x-4\right]\)
\(=\left(x+5\right)\left(5x-3\right)\)
b) \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left[2.\left(ab+2\right)\right]^2\)
\(=\left(a^2+b^2-5\right)^2-\left(2ab+4\right)^2\)
\(=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\)
\(=\left[\left(a-b\right)^2-9\right].\left[\left(a+b\right)^2-1\right]\)
\(=\left[\left(a-b-3\right)\left(a-b+3\right)\right].\left[\left(a+b-1\right)\left(a+b+1\right)\right]\)
a) \(3x^2+9x-30\)
\(=3\left(x^2+3x-10\right)\)
\(=3\left(x^2-2x+5x-10\right)\)
\(=3.\left[x\left(x-2\right)+5.\left(x-2\right)\right]\)
\(=3.\left[\left(x+5\right)\left(x-2\right)\right]\)
b) \(x^3-5x^2-14x\)
\(=x\left(x^2-5x-14\right)\)
\(=x\left(x^2+2x-7x-14\right)\)
\(=x.\left[x\left(x+2\right)-7.\left(x+2\right)\right]\)
\(=x.\left[\left(x-7\right)\left(x+2\right)\right]\)
= \(5x^3-2x^2-10x^2+4x+10x-4\)
= \(5x^2\left(x-\frac{2}{5}\right)-10x\left(x-\frac{2}{5}\right)+10\left(x-\frac{2}{5}\right)\)
=\(\left(x-\frac{2}{5}\right)\left(5x^2-10x+10\right)\)
Chuc ban hoc tot!
a) \(x^3y^3+x^2y^2+4\)
\(=x^3y^3-x^2y^2+2x^2y^2-2xy+2xy+4\)
\(=\left(x^3y^3-x^2y^2+2xy\right)+\left(2x^2y^2-2xy+4\right)\)
\(=xy\left(x^2y^2-xy+2\right)+2\left(x^2y^2-xy+2\right)\)
\(=\left(xy+2\right)\left(x^2y^2-xy+2\right)\)
b) \(x^3+3x^2y-9xy^2+5y^3\)
\(=x^3+5x^2y-2x^2y-10xy^2+xy^2+5y^3\)
\(=\left(5y^3-10xy^2+5x^2y\right)+\left(xy^2-2x^2y+x^3\right)\)
\(=5y\left(y^2-2xy+x^2\right)+x\left(y^2-2xy+x^2\right)\)
\(=\left(5y+x\right)\left(y^2-2xy+x^2\right)\)
\(=\left(5y+x\right)\left(y-x\right)^2\)
a) xy+3x-7y-21
=x(y+3)-7(x+3)
=(x-7)(y+3)
b)2xy-15-6x-5y
=2x(y-3)-5(-3+y)
=(2x-5)(y-3)
c)2x^2y+2xy^2-2x-2y
=2x(xy-1)+2y(xy-1)
=(2x+2y)(xy-1)
x(x+3)-5x(x-5)-5(x+3)
=(x-5)(x+3)-5x(x-5)
=(x-5)(x+3-5x)
Câu cuối mình bị nhầm dòng cuối phải là (x-5)(x+3+x-5)=(x-5)(2x-2)nha bạn
chưa trả lời mà đã thanks