Test: Algebraic expressions II - Challenging

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Question 1:   Divide x 3 -3 x 2 +4x-2 by x-1
x 2 -2x+2
x 2 -x
x 2 -x+2
x 2 +2x+2
Question 2:   Factorise: x 3 -11 x 2 +38x-40
( x-2 )( x-4 )( x-5 )
( x-2 )( x-3 )( x-5 )
( x-2 )( x 2 -9x+20 )
( x-2 ) ( x-5 ) 2
Question 3:   Simplify 1- m 1+ 1 1- 1 m and find value when m=3
- 1 5
0
1 5
1
Question 4:   Simplify expression and find its domain: x 2 -4x+4 - x 2
{ 2,x( -;0 ) -2x+2,x[ 0;2 ) -2,x[ 2;+ )
-2
-2x+2
2
Question 5:   Divide x 3 -11 x 2 +33x-20 by x 2 -7x+5
x-5
x-3
x-4
x 2 -2x+5
Question 6:   Find value of expression 9 y 2 + x 2 x 2 -xy if x y =3
2
1
3
0
Question 7:   Factorise: ( x 2 +x+1 )( x 2 +x+3 )-20
( x 2 +x+7 )( x-1 )
( x 2 +x+7 )( x+2 )( x-1 )
( x 2 +x+7 )( x+2 )
( x 2 +x+7 )( x 2 +x-2 )
Question 8:   Simplify expression ( y 16x- x 3 - 1 x 2 +4x + 4 x 2 y-16y )÷ y 2 -8y+16 x 3 y-16xy and find value if x=0,y=5
-2
0
1
-5
Question 9:   Simplify: ( x 2 - y 2 )÷( x -1 - y -1 )
( x+y ) xy
-xy( x+y )
xy( x+y )
xy ( x+y )
Question 10:   Simplify: ( x+ 1 3 ) ( 3+ 1 x ) -1
1
3x
3 x
x 3