Bài 1: 

a: \(11x^2-6xy-5y^2\)

\(=11x^2-11xy+5xy-5y^2\)

\(=11x\left(x-y\right)+5y\left(x-y\right)\)

\(=\left(x-y\right)\left(11x+5y\right)\)

b: \(4x^3-16x^2+19x-6\)

\(=4x^3-8x^2-8x^2+16x+3x-6\)

\(=\left(x-2\right)\left(4x^2-8x+3\right)\)

\(=\left(x-2\right)\left(2x-1\right)\left(2x-3\right)\)

Bài 1: 

a: \(11x^2-6xy-5y^2\)

\(=11x^2-11xy+5xy-5y^2\)

\(=11x\left(x-y\right)+5y\left(x-y\right)\)

\(=\left(x-y\right)\left(11x+5y\right)\)

b: \(4x^3-16x^2+19x-6\)

\(=4x^3-8x^2-8x^2+16x+3x-6\)

\(=\left(x-2\right)\left(4x^2-8x+3\right)\)

\(=\left(x-2\right)\left(2x-3\right)\left(2x-1\right)\)

\(a,=11x^2-11xy+5xy-5y^2=\left(11x+5y\right)\left(x-y\right)\\ b,=4x^3-8x^2-8x^2+16x+3x-6\\ =\left(x-2\right)\left(4x^2-8x+3\right)\\ =\left(x-2\right)\left(4x^2-2x-6x+3\right)\\ =\left(x-2\right)\left(2x-1\right)\left(2x-3\right)\)

Bài 1: 

a: \(11x^2-6xy-5y^2\)

\(=11x^2-11xy+5xy-5y^2\)

\(=11x\left(x-y\right)+5y\left(x-y\right)\)

\(=\left(x-y\right)\left(11x+5y\right)\)

b: \(4x^3-16x^2+19x-6\)

\(=4x^3-8x^2-8x^2+16x+3x-6\)

\(=\left(x-2\right)\left(4x^2-8x+3\right)\)

\(=\left(x-2\right)\left(2x-1\right)\left(2x-3\right)\)

c: \(x^4+x^3-4x^2+x+1\)

\(=x^4-x^3+2x^3-2x^2-2x^2+2x-x+1\)

\(=\left(x-1\right)\left(x^3+2x^2-2x-1\right)\)

\(=\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+2x\left(x-1\right)\right]\)

\(=\left(x-1\right)^2\cdot\left(x^2+3x+1\right)\)

Nếu ol thì tham khảo nah nguoiemtinhthong.

1.1

2x2+5x−1=7x3−1−−−−−√2x2+5x−1=7x3−1

⇔2(x2+x+1)+3(x−1)−7(x−1)(x2+x+1)−−−−−−−−−−−−−−−√(1)⇔2(x2+x+1)+3(x−1)−7(x−1)(x2+x+1)(1)

Đặt a=x−1−−−−−√;b=x2+x+1−−−−−−−−√;a≥0;b>0a=x−1;b=x2+x+1;a≥0;b>0

pt (1) trở thành 3a2+2b2−7ab=03a2+2b2−7ab=0

a=2ba=2b v a=13ba=13b

Các bạn tự giải quyết tiếp nhé.

1.2

TXĐ D=[1;+∞)D=[1;+∞)

đặt a=x−1−−−−−√4;b=x+1−−−−−√4;a,b≥0a=x−14;b=x+14;a,b≥0

pt (2) trở thành 3a2+2b2−5ab=03a2+2b2−5ab=0

⇔a=b⇔a=b v a=23ba=23b

...

1.3

D=[3;+∞)D=[3;+∞)

Đặt a=x2+4x−5−−−−−−−−−√;b=x−3−−−−−√;a,b≥0a=x2+4x−5;b=x−3;a,b≥0

pt (3) trở thành 3a+b=11a2−19b2−−−−−−−−−√3a+b=11a2−19b2

⇔2a2−6ab−20b2=0⇔2a2−6ab−20b2=0

⇒a=5b⇒a=5b
...

1.4

ĐK

⇔2x2−2x+2=3(x−2)x(x+1)−−−−−−−−−−−−√2x2−2x+2=3(x−2)x(x+1)

⇔(x2−2x)+2(x+1)=3(x2−2x)(x+1)−−−−−−−−−−−−−√2(x2−2x)+2(x+1)=3(x2−2x)(x+1)

Đặt x2−2x−−−−−−√=ax2−2x=a; x+1−−−−−√=bx+1=b (a;b\geq0)

⇔2a2+2b2=3ab

1.5

Đặt 4x2−4x−10=t4x2−4x−10=t (t \geq 0)

⇔t=t+4x2−2x−−−−−−−−−−√t=t+4x2−2x

⇔t2−t−4x2+2x=0t2−t−4x2+2x=0

Δ=1−4(2x−4x2)=(4x−1)2Δ=1−4(2x−4x2)=(4x−1)2

⇒t=1−2xt=1−2x hoặc t=2xt=2x

1.1

2.2+5.-1=7.3-1-----v2.2+5.-1=7.3-1

2(.2+x+1)+3(x-1)

3a+b=11a2-19b2

tóm tắt

\(A=4x\left(x^2-2x+1\right)=4x\left(x-1\right)^2\\ B=\left(x-y\right)^2-16=\left(x-y-4\right)\left(x-y+4\right)\\ C=\left(x-2\right)\left(x^2+2x+4\right)+3\left(x-2\right)=\left(x-2\right)\left(x^2+2x+7\right)\)

a) \(A=4x\left(x^2-2x+1\right)=4x\left(x-1\right)^2\)

b) \(B=\left(x^2-2xy+y^2\right)-16=\left(x-y\right)^2-16=\left(x-y-4\right)\left(x-y+4\right)\)

c) \(C=\left(x-2\right)\left(x^2+2x+4\right)+3\left(x-2\right)=\left(x-2\right)\left(x^2+2x+7\right)\)

\(a,N\left(x\right)=x^2+3x^4-2x-x^2+2x^3=3x^4+2x^3+\left(x^2-x^2\right)-2x\\ =3x^4+2x^3-2x\\ P\left(x\right)=-8+5x-6x^3-4x+6=-6x^3+\left(5x-4x\right)+\left(-8+6\right)\\ =-6x^3+x-2\)

Bậc của N(x) là 4

Bậc của P(x) là 3

\(b,P\left(x\right)+N\left(x\right)=3x^4+2x^3-2x-6x^3+x-2\\ =3x^4+\left(2x^3-6x^3\right)+\left(-2x+x\right)-2\\ =3x^4-4x^3-x-2\)

\(c,B\left(x\right)=-2x^2\left(x^3-2x+5x^2-1\right)\\ =\left(-2x^2\right).x^3+\left(-2x^2\right).\left(-2x\right)+\left(-2x^2\right).5x^2+\left(-2x^2\right).\left(-1\right)\\ =-2x^5+4x^3-10x^4+2x^2\\ =-2x^5-10x^4+4x^3+2x^2\)

\(a,=x\left(x+y\right)+5\left(x+y\right)=\left(x+5\right)\left(x+y\right)\\ b,=x\left(y-x\right)-3\left(y-x\right)=\left(x-3\right)\left(y-x\right)\\ c,=18x-4x^3=2x\left(9-2x^2\right)\\ d,=\left(x-2\right)^2-4y^2=\left(x-2y-2\right)\left(x+2y-2\right)\\ e,=x^2-x-9x+9=\left(x-1\right)\left(x-9\right)\\ f,=4x^2-6x+2x-3=\left(2x-3\right)\left(2x+1\right)\)

a: \(=x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-1\right)\)

b: \(=25-\left(x-2y\right)^2\)

\(=\left(5-x+2y\right)\left(5+x-2y\right)\)

\(a,=y\left(y-2\right)\\ b,=3x\left(x^2-2x+1\right)=3x\left(x-1\right)^2\\ c,=\left(y-1\right)\left(27x^2+9x^3\right)=9x^2\left(x+3\right)\left(y-1\right)\\ d,=y\left(y^2-2y+1\right)=y\left(y-1\right)^2\\ e,=x\left(x^2+6x+9\right)=x\left(x+3\right)^2\\ f,=x\left(x^2-2xy+y^2\right)=x\left(x-y\right)^2\\ g,=\left(2-x\right)\left(x+1\right)\\ h,=\left(x-1\right)\left(3x-6\right)=3\left(x-1\right)\left(x-2\right)\)

a: =y(y-2)

b: \(=3x^2\left(x^2-2x+1\right)=3x^2\left(x-1\right)^2\)

d: \(=y\left(y^2-2y+1\right)=y\left(y-1\right)^2\)