Question

1) Calculati :
a) 6/5-11/4+1/10
b) [3/5-(-1/5)^2] : (1/10-1 1/2)^2
c) [0,(12)-1/11] : 0,(06)
d) 0,2:1/4+2/5*1,5+5^-1
2) x^2+6x+8
X^2-10x-24
X^2-12x+32
X^2+3x-40

Answer 1

a) 6/5-11/4+1/10 =
=(24-55+2)/20=
=-29/20

b) [3/5-(-1/5)²] : (1/10-1 1/2)²=
=(3/5-1/25) : (1/10-3/2)²=
=(15-1)/25 : [(1-15)/2]²=
=14/25:(-14/2)²=
=14/25:196/4=
=14/25 x4/196=
=100/14=50/7

c) [0,(12)-1/11] : 0,(06)=
0,(12)=12/99=4/33
0,(06)=6/99=2/33
= [4/33-1/11] : 2/33=
=(4-3)/33 x33/2=
=1/33 x33/2=
=1/2

d) 0,2:1/4+2/5*1,5+5⁻¹=
=1/5 x4/1 + 3/5+1/5=
=4/5+4/5=8/5

2) x²+6x+8 =x²+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)

X²-10x-24 =x²-12x+2x-24=x(x-12)+2(x12)=(x-12)(x+2)

X²-12x+32=x²-8x-4x+32=x(x-8)-4(x-8)=(x-8)(x-4)

X²+3x-40=x²-5x+8x-40=x(x-5)+8(x-5)=(x-5)(x+8)