Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Rewrite the rational expression 2x^3-7x^2+6x-9/x-3 in the form q(x)+r(x)/b(x) in nikki. Then match q(x), r(x), and b(x) to the correct expressions.​

Answer 1

whats the answer fo q(x)

Explanation:

Answer 2

The given expression can be written in the form
`q(x)+(r(x))/(b(x))` as
`(2x^2-x+3)+(0)/(x-3)` where q(x)=
`2x^2-x+3` , r(x)=0 and b(x)=x-3

Explanation:

Given rational expression is
`(2x^3-7x^2+6x-9)/(x-3)`

To rewrite the given rational expression in the given form and match their correct expressions:

Rewrite the given rational expression
`(2x^3-7x^2+6x-9)/(x-3)` in the form of
`q(x)+(r(x))/(b(x))` where q(x) is the quotient, r(x) is the remainder and b(x) is the divisor.

Now solve the given expression by using Synthetic division, we get

Since x-3 is a factor for
`2x^3-7x^2+6x-9`

Therefore b(x)=x-3

3_| 2 -7 6 -9

0 6 -3 9

------------------------------------

2 -1 3 0

------------------------------------

Therefore we have quadratic equation
`2x^2-x+3=0`

q(x)=
`2x^2-x+3`

Remainder is 0

Therefore r(x)=0

Therefore we can write in the form as
`(2x^2-x+3)+(0)/(x-3)`

It is in the form of
`q(x)+(r(x))/(b(x))`

Therefore the given expression can be written in the form
`q(x)+(r(x))/(b(x))` as
`(2x^2-x+3)+(0)/(x-3)` where q(x)=
`2x^2-x+3` , r(x)=0 and b(x)=x-3