Answer:
[tex]k^2-30k-18-4k^2=(k+3)(-3k-21)+45[/tex]
Step-by-step explanation:
Given:
[tex](k^2-30k-18-4k^2):(3+k)[/tex]
Consider the expression [tex]k^2-30k-18-4k^2[/tex]. First, add the like term [tex]k^2[/tex] and [tex]-4k^2:[/tex]
[tex]k^2-4k^2=-3k^2[/tex]
Now, this expression is
[tex]-3k^2-30k-18[/tex]
Divide [tex]-3k^2-30k-18[/tex] by [tex]k+3.[/tex] Multiply [tex]k+3[/tex] by [tex]-3k[/tex] and subtract the result from the [tex]-3k^2-30k-18[/tex] to eliminate the highest term [tex]-3k^2:[/tex]
[tex]-3k^2-30k-18-(-3k)(k+3)=-3k^2-30k-18+3k^2+9k=-21k-18[/tex]
Multiply [tex]k+3[/tex] by -21 and subtract the result from [tex]-21k-18:[/tex]
[tex]-21k-18-(-21)(k+3)=-21k-18+21k+63=45[/tex]
Hence,
[tex]k^2-30k-18-4k^2=(k+3)(-3k-21)+45[/tex]
