Question

(K² – 30k - 18 - 4K²) ÷ (3+k).​

Answer 1

Answer:

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

Step-by-step 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,

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