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1.2x^2+x-6=2x^2+4x-3x+6=(2x^2+4x)-(3x+6)=2x(x+2)-3(x+2)=(x+2)(2x-3)
2.x^3-9x^2+14x
=x*(x^2-9x+14)
=x*(x^2-7x-2x+14)
=x*((x^2-7x)-(2x-14))
=x*(x(x-7)-2(x-7))
=x*((x--7)(x-2))
=x*(x-7)(x-2)
p/ x4 - 9x3 + 22x2 - 9x + 1
= (x4 - 5x3 + x2) + (- 4x3 + 20x2 - 4x) + (x2 - 5x + 1)
= (x2 - 5x + 1)(x2 - 4x + 1)
q) x4 - 6x3 + 14x2 - 22x + 5
= (x4 - 4x3 + x2) + (- 2x3 + 8x2 - 2x) + (5x2 - 20x + 5)
= (x2 - 4x + 1)(x2 - 2x + 5)
1.2x^2+x-6=2x^2+4x-3x+6=(2x^2+4x)-(3x+6)=2x(x+2)-3(x+2)=(x+2)(2x-3)
2.x^3-9x^2+14x
=x*(x^2-9x+14)
=x*(x^2-7x-2x+14)
=x*((x^2-7x)-(2x-14))
=x*(x(x-7)-2(x-7))
=x*((x--7)(x-2))
=x*(x-7)(x-2)
1)
\(=\left(x-7\right)^2-4a^2\)
\(=\left(x-7+2a\right)\left(x-7-2a\right)\)
2)
\(=\left(3x+1\right)^2-5^2\)
\(=\left(3x+1+5\right)\left(3x+1-5\right)\)
\(=\left(3x+6\right)\left(3x-4\right)\)
\(=3\left(x+2\right)\left(3x-4\right)\)
1)x^2-14x+49-4a^2
=x^2-2x7+7^2-4a^2
=\(\left(x-7\right)^2-4a^2\)
=\(\left(x-7\right)^2-\left(2a\right)^2\)
=\(\left(\left(x-7\right)-\left(2a\right)\right).\left(\left(x-7\right)+\left(2a\right)\right)\)
=\(\left(x-7-2a\right).\left(x-7+2a\right)\)
b)
\(9x^2+6x+1-25\\ =\left(3x\right)^2-5^2+6x+1\\ =\left(\left(3x\right)-5\right).\left(\left(3x\right)+5\right)+6x+1\)
\(=\left(3x-5\right).\left(3x+5\right)+6x+1\)
A) 7X2 - 7Y2 - 14X + 14Y
= ( 7X2 - 7Y2 ) - ( 14X - 14Y )
= 7( X2 - Y2 ) - 14( X - Y )
= 7( X - Y )( X + Y ) - 14( X - Y )
= 7( X - Y )( X + Y - 14 )
B) X2 - Y2 + 14X + 49
= ( X2 + 14X + 49 ) - Y2
= ( X + 7 )2 - Y2
= ( X - Y + 7 )( X + Y + 7 )
C) X2 - Y2 - X + Y
= ( X2 - Y2 ) - ( X - Y )
= ( X - Y )( X + Y ) - ( X - Y )
= ( X - Y )( X + Y - 1 )
D) X2 + 12Y - Y2 - 36
= X2 - ( Y2 - 12Y + 36 )
= X2 - ( Y - 6 )2
= ( X - Y + 6 )( X + Y - 6 )
E) X3 + X2 - 9X - 9
= ( X3 + X2 ) - ( 9X + 9 )
= X2( X + 1 ) - 9( X + 1 )
= ( X + 1 )( X2 - 9 )
= ( X + 1 )( X - 3 )( X + 3 )
Ta có: x2y+5xy-14y
= y(x2+5x-14)
= y(x+7)(x-2)
x3-5x2-14x
= x(x2-5x-14)
= x(x-7)(x+2)
\(x^2y+5xy-14y\)
\(=x^2y-2xy+7xy-14y\)
\(=xy\left(x-2\right)+7y\left(x-2\right)\)
\(=\left(x-2\right)\left(xy+7y\right)\)
\(x^3-5x^2-14x\)
\(=x^3-7x^2+2x^2-14x\)
\(=x^2\left(x-7\right)+2x\left(x-7\right)\)
\(=\left(x^2+2x\right)\left(x-7\right)\)
\(=x\left(x+2\right)\left(x-7\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a)\(3x^2-5x-2=3x^2-6x+x-2=3x\left(x-2\right)+\left(x-2\right)\)
\(=\left(3x+1\right)\left(x-2\right)\)
\(x^3-9x^2+14x=x\left(x^2-9x+14\right)\)
\(=x\left(x^2-2x-7x+14\right)=x\left(x\left(x-2\right)-7\left(x-2\right)\right)\)
\(=x\left(x-7\right)\left(x-2\right)\)