Rational expressions 2

Question 1

remainder theorum

(x³+4x²-x+8) / (x-2)

Answer 1

(x-2)(x²+6x+11)+30

Question 2

how to find the remainder

if p(x) is divided by (ax-b)

Answer 2

then the remainder will be whatever you get when you put x=a/b into the equation

Question 3

p(x) = (3x³+10x²-3x-2) / (3x+1)

simplify

Answer 3

p:(-1/3) =0

so 3x+1 is a factor

(3x+1)(x²+3x-2)/3x+1 = x²+3x-2

Question 4

if numerator > denominator

Answer 4

then further division is required

Question 5

simplify: x+6/x-2

Answer 5

x-2+8/x-2

= x-2/x-2 + 8/x-2

= 1+ 8/x-2

Question 6

simplify: x²+6x-3/x+2

and check remainder

Answer 6

(x+2)(x+4)-11/x+2

=x+4 - 11/x+2

to check: x+2=0 so x= -2 put into x²+6x-3, it gives -11

Question 7

simplify: 2x³ +5x²-x+4 /2x-1 =

Answer 7

(2x-1)(x²+3x+1)+5

x²+3x+1 +(5/2x-1)

use remainder theorum of x=1/2 too check remainder is 5

Question 8

simplify: x³-2x²+x+5/x²-3

Answer 8

[(x²-3)(x-2) +4x-1]/x²-3

4x-1 being the remainder

x-2 + (4x-1)/x²-3

Question 9

simplify: 2x²+2x+3/x²+x

Answer 9

2 + 3/(x²+x)