Question

(K² – 30k - 18 - 4K²) ÷ (3+k).​

Answer 1

`k^2-30k-18-4k^2=(k+3)(-3k-21)+45`

Explanation:

Given:

`(k^2-30k-18-4k^2):(3+k)`

Consider the expression
`k^2-30k-18-4k^2`. First, add the like term
`k^2` and
`-4k^2:`

`k^2-4k^2=-3k^2`

Now, this expression is

`-3k^2-30k-18`

Divide
`-3k^2-30k-18` by
`k+3.` Multiply
`k+3` by
`-3k` and subtract the result from the
`-3k^2-30k-18` to eliminate the highest term
`-3k^2:`

`-3k^2-30k-18-(-3k)(k+3)=-3k^2-30k-18+3k^2+9k=-21k-18`

Multiply
`k+3` by -21 and subtract the result from
`-21k-18:`

`-21k-18-(-21)(k+3)=-21k-18+21k+63=45`

Hence,

`k^2-30k-18-4k^2=(k+3)(-3k-21)+45`