Question

x+5÷5x⁴+8x³+3x+10
X²+2÷8x⁵+6x⁴+4x²+8

Answer 1

Your questions needs a bit improvement.

Here, the places of divisor and dividend are to be exchanged.

Therefore we've :

5x⁴+8x³+3x+10÷x+5 and

8x⁵+6x⁴+4x²+8÷x²+2

Now let's go :

1.) 5x⁴+8x³+3x+10÷x+5:

Step 1: Divide the term with highest power of x in dividend by the term with highest power in divisor and then multiply the quotient by divisor and then subtract whatever you get from the dividend.

i.e. :

$(5{x}^{4}+8{x}^{3}+3x+10) - \frac{5 {x}^{4} }{x} \times (x + 5)$

Note down whatever we get.

$- 17 {x}^{3} + 3x + 10$

Step 2: Now again repeat the step one :

$( - 17{x}^{3} + 3x + 10) - \frac{( - 17 {x}^{3} )}{x} \times (x + 5)$

and note down whatever you get :

$85 {x}^{2} + 3x + 10$

Step 3: Again repeat the step :

$(85 {x}^{2} + 3x + 10) - \frac{85 {x}^{2} }{x} \times (x + 5)$

and note down whatever you get :

$- 422x + 10$

Step 4: Repeat the step again:

$( - 422x + 10) - \frac{( - 422x)}{x} \times (x + 5)$

and note down whatever you get:

$2120$

Step 5: Here it can't be further divided by x so it's the remainder...

and for quotient note down the the numbers with which you have multiplied (x+5) in each step and add them together...

therefore we've quotient is:

$5 {x}^{3} - 17 {x}^{2} + 85x - 422$

Do the same to solve the next one .

Answer is been too lengthy because it's all what can I explain by writing only. However, hope it helps.