Question

(50k³ + 10k² − 35k – 7) ÷ (5k − 4)How do I simplify this problem

Answer 1

`10k^(2)+10k+1-(3)/(5k-4)`

EXPLANATION :

From the problem, we have an expression :

`(50k^3+10k^2-35k-7)/(5k-4)`

The divisor is (5k - 4)

Step 1 :

Divide the 1st term by the first term of the divisor.

`(50k^3)/(5k)=10k^2`

The result is 10k^2

Step 2 :

Multiply the result to the divisor :

`10k^2(5k-4)=50k^3-40k^2`

Step 3 :

Subtract the result from the polynomial :

`(50k^3+10k^2-35k-7)-(50k^3-40k^2)=50k^2-35k-7`

Now we have the polynomial :

`50k^2-35k-7`

Repeat Step 1 :

`(50k^2)/(5k)=10k`

The result is 10k

Repeat Step 2 :

`10k(5k-4)=50k^2-40k`

Repeat Step 3 :

`(50k^2-35k-7)-(50k^2-40k)=5k-7`

Now we have the polynomial :

`5k-7`

Repeat Step 1 :

`(5k)/(5k)=1`

The result is 1

Repeat Step 2 :

`1(5k-4)=5k-4`

Repeat Step 3 :

`(5k-7)-(5k-4)=-3`

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 :

`\begin{gathered} 10k^2+10k+1+(-3)/(5k-4) \\ or \\ 10k^2+10k+1-(3)/(5k-4) \end{gathered}`