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\(b,x^3-3x^2-4x+12\)
\(\Leftrightarrow x^2\left(x-3\right)-4\left(x-3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x^2-4\right)\)
\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
\(c,3x^3-7x^2+17x-5\)
\(\Leftrightarrow3x^3-x^2-6x^2+2x+15x-5\)
\(\Leftrightarrow x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)
\(\Leftrightarrow\left(3x-1\right)\left(x^2-2x+5\right)\)
\(\text{d) 2x}^4- 7x^3 - 2x^2 + 13x + 6\)
\(\text{= (2x^4 + 2x^3) - (9x^3 + 9x^2) + (7x^2 + 7x) + (6x + 6)}\)
\(\text{= 2x^3(x + 1) - 9x^2(x + 1) + 7x(x + 1) + 6(x + 1)}\)
\(\text{= (x + 1)(2x^3 - 9x^2 + 7x + 6)}\)
\(\text{= (x + 1)(2x + 1)(x - 3)(x - 2)}\)
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).
a)\(x^2+10x+25-y^2\)
\(=\left(x+5\right)^2-y^2\)
\(=\left(x+5+y\right)\left(x+5-y\right)\)
b)\(5x^3-7x^2+10x-14\)
\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)
\(=\left(x^2+2\right)\left(5x-7\right)\)
c)\(-5y^2+30y-45\)
\(=-5\left(y^2-6y+9\right)\)
\(=-5\left(y-3\right)^2\)
e)\(4xy^2-8xyz+4xz^2\)
\(=4x\left(y^2-2yz+z^2\right)\)
\(=4x\left(y-z\right)^2\)
f)\(x^2+7x+10\)
\(=x^2+5x+2x+10\)
\(=x\left(x+5\right)+2\left(x+5\right)\)
\(=\left(x+2\right)\left(x+5\right)\)
k)\(2x^7+6x^6+6x^5-2x^4\)
\(=2x^4\left(x^3+3x^2+3x-1\right)\)
a)\(x^2+10x+25-y^2\)
\(=\left(x+5\right)^2-y^2\)
\(=\left(x+5-y\right)\left(x+5+y\right)\)
b)\(5x^3-7x^2+10x-14\)
\(=x^2\left(5x-7\right)+2\left(5x-7\right)\)
\(=\left(5x-7\right)\left(x^2+2\right)\)
c)\(-5y^2+30y-45\)
\(=-5\left(y^2-6y+9\right)\)
\(=-5\left(y-3\right)^2\)
e)\(4xy^2-8xyz+4xz^2\)
\(=4x\left(y^2-2yz+z^2\right)\)
\(=4x\left(y-z\right)^2\)
f)\(x^2+7x+10\)
\(=x^2+5x+2x+10\)
\(=x\left(x+5\right)+2\left(x+5\right)\)
k)\(2x^7+6x^6+6x^5-2x^4\)
\(=2x^4\left(x^3+3x^2+3x-1\right)\)
\(=\left(x+2\right)\left(x+5\right)\)
a) \(x^3-2x^2+5x-4\)
\(=x^3-x^2-x^2+x+4x-4\)
\(=x^2\left(x-1\right)-x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-x+4\right)\)
b) \(x^3-x^2+x+3=\left(x+1\right)\left(x^2-2x+3\right)\)
c) \(x^3-6x^2-9x+14=\left(x-7\right)\left(x-1\right)\left(x+2\right)\)
d) \(x^4+2x^2-3=\left(x-1\right)\left(x+1\right)\left(x^2+3\right)\)
a) x3−2x2+5x−4�3−2�2+5�−4
=x3−x2−x2+x+4x−4=�3−�2−�2+�+4�−4
=x2(x−1)−x(x−1)+4(x−1)=�2(�−1)−�(�−1)+4(�−1)
=(x−1)(x2−x+4)
\(1.\)
\(4x^2-4x-3\)
\(=4x^2-2x+6x-3\)
\(=2x\left(2x-1\right)+3\left(2x-1\right)\)
\(=\left(2x+3\right)\left(2x-1\right)\)
\(2.\)
\(2x^2-5x-3\)
\(=2x^2-6x+x-3\)
\(=2x\left(x-3\right)+\left(x-3\right)\)
\(=\left(2x+1\right)\left(x-3\right)\)
\(3.\)
\(3x^2-5x-2\)
\(=3x^2+x-6x-2\)
\(=x\left(3x+1\right)-2\left(3x+1\right)\)
\(=\left(3x+1\right)\left(x-2\right)\)
\(4.\)
\(2x^2+5x+2\)
\(=2x^2+4x+x+2\)
\(=2x\left(x+2\right)+\left(x+2\right)\)
\(=\left(2x+1\right)\left(x+2\right)\)
\(5.\)
\(6x^2-x-1\)
\(=6x^2-3x+2x-1\)
\(=2x\left(3x+1\right)-\left(3x+1\right)\)
\(=\left(2x-1\right)\left(3x+1\right)\)
\(6.\)
\(6x^2-6x-3\)
\(=3\left(2x^2-2x-1\right)\)
\(7.\)
\(15x^2-2x-1\)
\(=15x^2+3x-5x-1\)
\(=3x\left(5x+1\right)-1\left(5x+1\right)\)
\(=\left(5x+1\right)\left(3x-1\right)\)
\(8.\)
\(x^4-13x^2+36\)
\(=\left(x-3\right)\left(x^3+3x^2-4x-12\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x^2+5x+6\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)\)
a/ \(=x^2+2x-7x-14=x\left(x+2\right)-7\left(x+2\right)=\left(x-7\right)\left(x+2\right)\)
b/ \(=15-3x=3\left(5-x\right)\)
c/ \(=x^2-3xy-4xy+12y^2=x\left(x-3y\right)-4y\left(x-3y\right)=\left(x-4y\right)\left(x-3y\right)\)
d/ \(=x^3-2x^2+x+2x^2-4x+2=x\left(x^2-2x+1\right)+2\left(x^2-2x+1\right)=\left(x+2\right)\left(x-1\right)^2\)
a)x2-5x-14=(x2-7x)+(2x-14)=x(x-7)+2(x-7)=(x-7)(x+2)
b)4x2-3x-1=(4x2-4x)+(x-1)=4x(x-1)+(x-1)=(x-1)(4x+1)
c)x2-7xy+12y2=x2-7xy+12,25y2-0,25y2=(x-3,5y)2-0,25y2=(x-3,5y-0,5y)(x-3,5y+0,5y)=(x-4y)(x-2y)
d)x3-3x+2=(x3-x)-(2x-2)=(x-1)(x2+x)-2(x-1)=(x-1)(x2+x-2)=(x-1)(x2-2x+x-2)=(x-1)(x+1)(x-2)
a) x2 - 5x - 14 = x2 + 2x - 7x - 14 = x(x + 2) - 7(x + 2) = (x + 2)(x - 7)
b) 4x2 - 3x - 1 = 4x2 - 4x + x - 1 = 4x(x - 1) + (x - 1) = (x - 1)(4x + 1)
c) x2 - 7xy + 12y2 = x2 - 4xy - 3xy + 12y2 = x(x - 4y) - 3y(x - 4y) = (x - 4y)(x - 3y)
d) x2 - 3x + 2 = x2 - x - 2x - 2 = x(x - 1) - 2(x - 1) = (x - 1)(x - 2)
a ) \(x^2-13x+36\)
\(=x^2-4x-9x+36\)
\(=x\left(x-4\right)-9\left(x-4\right)\)
\(=\left(x-9\right)\left(x-4\right)\)
b ) \(x^2+5x-14\)
\(=x^2-2x+7x-14\)
\(=x\left(x-2\right)+7\left(x-2\right)\)
\(=\left(x+7\right)\left(x-2\right)\)
c ) \(2x^2-5x-12\)
\(=2x^2-8x+3x-12\)
\(=2x\left(x-4\right)+3\left(x-4\right)\)
\(=\left(2x+3\right)\left(x-4\right)\)
d ) \(x^2-4xy-12y^2\)
\(=x^2-4xy+4y^2-16y^2\)
\(=\left(x-2y\right)^2-\left(4y\right)^2\)
\(=\left(x-2y-4y\right)\left(x-2y+4y\right)\)
\(=\left(x-6y\right)\left(x+2y\right)\)
a) x2-13x+36
=x2-4x-9x+36
=(x2-4x)-(9x-36)
=x(x-4)-9(x-4)
=(x-4)(x-9)
b) x2+5x-14
=x2+7x-2x-14
=(x2+7x)-(2x+14)
=x(x+7)-2(x+7)
=(x+7)(x-2)
c) 2x2-5x-12
=2x2+3x-8x-12
=(2x2+3x)-(8x+12)
=x(2x+3)-4(2x+3)
=(2x+3)(x-4)
d) x2-4xy-12y2
=x2-4xy+4y2-16y2
=(x2-4xy+4y2)-16y2
=(x-2y)2-16y2
=(x-2y-4y)(x-2y+4y)
=(x-6y)(x+2y)