1.12
a)
4x²+4x+1=4x²+2z+2x+1=2x(2x+1)+1(2x+1)=(2x+1)(2x+1)
3x-1 ! (3x-1)(2x+1) ! 6x²+3x-2x-1 ! 6x²+x-1
______= ____________= ___________ = __________
2x+1 ! (2x+1)(2x+1) ! 4x²+2z+2x+1 ! 4x²+4x+1
b)
2x²-3x-2=2x²+x-4x-2=x(2x+1)-2(2x+1)=(2x+1)(x-2)
3x-1 ! (3x-1)(x-2) ! 3x²-6x-x+2 ! 3x²-7x+2
______= ____________= ___________ = __________
2x+1 ! (2x+1)(x-2) ! 2x²+x-4x-2 ! 2x²-3x-2
c)
-2x²+5x+3=-2x²-x+6x+3=-x(2x+1)(-x+3)
3x-1 ! (3x-1)(-x+3) ! -3x²-9x+x-3 ! -3x²-8x-3
______= ____________= ___________ = __________
2x+1 ! (2x+1)(-x+3) ! -2x²-x+6x+3 ! -2x²+5x+3
d)
2x³+x²-6x-3=x²(2x+1)-3(2x+1)=(x²-3)(2x+1)
3x-1 ! (3x-1)(x²-3) ! 3x³-9x-x²+3
______= ____________= ___________
2x+1 ! (2x+1)(x²-3) ! 2x³+x²-6x-3
1.13
a)
4x-2 ! (4x-2)(4x+2) ! 16x²-4
______= ____________ = ___________
2x²+3x ! (2x²+3x)(4x+2) ! 8x³+16x²+6x
b)
4x-2 ! (4x-2) (4x-2) ! 16x²-4
______= ____________ = ___________
2x²+3x ! (2x²+3x)(4x-2) ! 8x³+8x²-6x
c)
4x-2 ! (4x-2)(-2x+3) ! -8x²+16x-6
______= ____________ = ___________
2x²+3x !(2x²+3x)(-2x+3) ! -4x³+9x
d)
4x-2 ! (4x-2)(x²+x+1) ! 4x³+2x²+2x-2
______= ____________ = ___________
2x²+3x !(2x²+3x)(x²+x+1) ! 2x⁴+5x³+5x² +3x
