Discover how IDNLearn.com can help you find the answers you need quickly and easily. Discover the information you need quickly and easily with our reliable and thorough Q&A platform.
Sagot :
ANSWER :
[tex]10k^{2}+10k+1-\frac{3}{5k-4}[/tex]
EXPLANATION :
From the problem, we have an expression :
[tex](50k^3+10k^2-35k-7)\div(5k-4)[/tex]The divisor is (5k - 4)
Step 1 :
Divide the 1st term by the first term of the divisor.
[tex]\frac{50k^3}{5k}=10k^2[/tex]The result is 10k^2
Step 2 :
Multiply the result to the divisor :
[tex]10k^2(5k-4)=50k^3-40k^2[/tex]Step 3 :
Subtract the result from the polynomial :
[tex](50k^3+10k^2-35k-7)-(50k^3-40k^2)=50k^2-35k-7[/tex]Now we have the polynomial :
[tex]50k^2-35k-7[/tex]Repeat Step 1 :
[tex]\frac{50k^2}{5k}=10k[/tex]The result is 10k
Repeat Step 2 :
[tex]10k(5k-4)=50k^2-40k[/tex]Repeat Step 3 :
[tex](50k^2-35k-7)-(50k^2-40k)=5k-7[/tex]Now we have the polynomial :
[tex]5k-7[/tex]Repeat Step 1 :
[tex]\frac{5k}{5k}=1[/tex]The result is 1
Repeat Step 2 :
[tex]1(5k-4)=5k-4[/tex]Repeat Step 3 :
[tex](5k-7)-(5k-4)=-3[/tex]Since -3 is a number, this will be the remainder.
Collect the bold results we had from above :
(10k^2 + 10k + 1) remainder -3
Note that the remainder can be expressed as remainder over divisor.
That will be :
[tex]\begin{gathered} 10k^2+10k+1+\frac{-3}{5k-4} \\ or \\ 10k^2+10k+1-\frac{3}{5k-4} \end{gathered}[/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com is your go-to source for dependable answers. Thank you for visiting, and we hope to assist you again.
