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1) x2 -7x + 10 = x2 - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 5)(x - 2)
2) x2 + 3x + 2 = x2 + 2x + x + 2 = x(x + 2) + (x + 2) = (x + 1)(x + 2)
3) x2 - 7x + 12 = x2 - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 3)(x - 4)
4) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4)
5) 16x - 5x2 - 3 = 15x - 5x2 + x - 3 = -5x(x - 3) + (x - 3) = (x - 3)(1 - 5x)
6) 6x2 + 7x - 3 = 6x2 - 2x + 9x - 3 = 2x(3x - 1) + 3(3x - 1) = (2x + 3)(3x - 1)
7) 3x2 - 3x - 6 = 3x2 - 6x + 3x - 6 = 3x(x - 2) + 3(x - 2) = (x - 2)(3x + 3) = 3(x - 2)(x + 1)
8) 3x2 + 3x - 6 = 3x2 - 3x + 6x - 6 = 3x(x - 1) + 6(x - 1) = (x - 1)(3x + 6) = 3(x - 1)(x + 2)
9) 6x2 - 13x + 6 = 6x2 - 9x - 4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3)
10) 6x2 + 15x + 6 = 6x2 + 12x + 3x + 6 = 6x(x + 2) + 3(x + 2) = (x + 2)(6x + 3) = 3(x + 2)(3x + 1)
11) 6x2 - 20x + 6 = 6x2 - 18x - 2x + 6 = 6x(x -3) - 2(x - 3) = (6x - 2)(x - 3) = 2(3x - 1)(x - 3)
12) 8x2 + 5x - 3 = 8x2 + 8x - 3x - 3 = 8x(x + 1) - 3(x + 1) = (x + 1)(8x - 3)
a, x2+2xy+y2+2x+2y-15
<=> (x+y )2+2(x+y)+1-16
Đặt x+y =a
<=> a2+2a+1-42
<=> (a+1)2-42
<=> (a+5)(a-3) =>( x+y+5)(x+y-3)
b, x2-4xy+4y2-2x-4y-35
<=> (x-2y)2-2(x-2y)+1-36
Đặt (x-2y) =b
=> b2-2b+1-62
<=> (b-1)2-62
<=> (b-7)(b+5)=> (x-2y-7)(x-2y+5)
c,
a,A= x^2+2xy+y^2+2x+2y-15
= (x+y)^2+(x+y)-15
Đặt x+y=a, ta có:
A=a^2+2a-15
=a^2+2a+1-16
=(a+1)^2-4^2
=(a+1+4)(a+1-4)
=(a+5)(a-3)
Thay a=x+y, ta có: A=(x+y+5)(x+y-3).
Cân lun!
\(x^4-10x^3-15x^2+20x+4\)
\(=x^4-x^3-9x^3+9x^2-24x^2+24x-4x+4\)
\(=x^3\left(x-1\right)-9x^2\left(x-1\right)-24x\left(x-1\right)-4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3-9x^2-24x-4\right)\)
\(=\left(x-1\right)\left(x^3+2x^2-11x^2-22x-2x-4\right)\)
\(=\left(x-1\right)\left[x^2\left(x+2\right)-11x\left(x+2\right)-2\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2-11x-2\right)\)
Chúc bạn học tốt!!!
a) x4+x3+2x2+x+1=(x4+x3+x2)+(x2+x+1)=x2(x2+x+1)+(x2+x+1)=(x2+x+1)(x2+1)
b)a3+b3+c3-3abc=a3+3ab(a+b)+b3+c3 -(3ab(a+b)+3abc)=(a+b)3+c3-3ab(a+b+c)
=(a+b+c)((a+b)2-(a+b)c+c2)-3ab(a+b+c)=(a+b+c)(a2+2ab+b2-ac-ab+c2-3ab)=(a+b+c)(a2+b2+c2-ab-ac-bc)
c)Đặt x-y=a;y-z=b;z-x=c
a+b+c=x-y-z+z-x=o
đưa về như bài b
d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung
e)x2(y-z)+y2(z-x)+z2(x-y)=x2(y-z)-y2((y-z)+(x-y))+z2(x-y)
=x2(y-z)-y2(y-z)-y2(x-y)+z2(x-y)=(y-z)(x2-y2)-(x-y)(y2-z2)=(y-z)(x2-2y2+xy+xz+yz)
a: Ta có: \(-3x^4+20x^3-35x^2-10x+48\)
\(=-\left(3x^4-20x^3+35x^2+10x-48\right)\)
\(=-\left(3x^4-9x^3-11x^3+33x^2+2x^2-6x+16x-48\right)\)
\(=-\left(x-3\right)\left(3x^3-11x^2+2x+16\right)\)
\(=-\left(x-3\right)\left(3x^3-6x^2-5x^2+10x-8x+16\right)\)
\(=-\left(x-3\right)\left(x-2\right)\left(3x^2-5x-8\right)\)
\(=-\left(x-3\right)\left(x-2\right)\left(3x-8\right)\left(x+1\right)\)
b: Ta có: \(-\left(2x^4+7x^3+x^2-7x-3\right)\)
\(=-\left(2x^4-2x^3+9x^3-9x^2+10x^2-10x+3x-3\right)\)
\(=-\left(x-1\right)\left(2x^3+9x^2+10x+3\right)\)
\(=-\left(x-1\right)\left(2x^3+2x^2+7x^2+7x+3x+3\right)\)
\(=-\left(x-1\right)\left(x+1\right)\left(2x^2+7x+3\right)\)
\(=-\left(x-1\right)\left(x+1\right)\cdot\left(x+3\right)\left(2x+1\right)\)
1) \(6x^2-15x+6\)
\(=6x^2-3x-12x+6\)
\(=3x\left(2x-1\right)-6\left(2x-1\right)\)
\(=\left(3x-6\right)\left(2x-1\right)\)
\(=3\left(x-2\right)\left(2x-1\right)\)
b) \(6x^2-20x+6\)
\(=6x^2-2x-18x+6\)
\(=2x\left(3x-1\right)-6\left(3x-1\right)\)
\(=\left(2x-6\right)\left(3x-1\right)\)
\(=2\left(x-3\right)\left(3x-1\right)\)
c) \(-10x^2-7x+6\)
\(=5x-10x^2+6-12x\)
\(=5x\left(1-2x\right)+6\left(1-2x\right)\)
\(=\left(5x+6\right)\left(1-2x\right)\)
d) \(10x^2-7x-12\)
\(=10x^2-15x+8x-12\)
\(=5x\left(2x-3\right)+4\left(2x-3\right)\)
\(=\left(5x+4\right)\left(2x-3\right)\)
1) 6x^2 - 15x + 6
= 6x^2 - 12x - 3x +6
= 6x (x - 2) - 3 (x - 2)
= (x - 2) (6x - 3)
= 3 (x - 2) (x - 1)
2) 6x^2 - 20x + 6
= 6x^2 - 18x - 2x + 6
= 6x (x - 3) - 2 (x - 3)
= (x - 3) (6x - 2)
= 2 (x - 3) (3x - 1)
3) -10x^2 - 7x + 6
= -10x^2 + 5x - 12x + 6
= 5x (1 - 2x) + 6 (1 - 2x)
= (1 - 2x) (5x + 6)
4) 10x^2 - 7x - 12
= 10x^2 - 15x + 8x - 12
= 5x (2x - 3) + 4 (2x - 3)
= (2x - 3) (5x + 4)
good luck !