Question

(5x2 − 22x + 8) ÷ (x − 4)?

Answer 1

`(5x^2-22x+8)/ (x-4)=5x-2`

Explanation:

The given expression is;

`(5x^2-22x+8)/ (x-4)`

This can be rewritten as

`(5x^2-22x+8)/(x-4)`

Factor the numerator by splitting the middle term;

`(5x^2-20x-2x+8)/(x-4)`

`(5x(x-4)-2(x-4))/(x-4)`

`((x-4)(5x-2))/((x-4))`

Cancel the common factors;

`5x-2`

`\therefore ](5x^2-22x+8)/ (x-4)=5x-2`

Answer 2

Let's use synthetic division to solve this problem. This method is applied for dividing polynomials by binomials of the form
`x-k`. These are the steps you must follows:

a) Take the coefficients of
`p(x)` and write them down in order.

b) Copy the leftmost coefficient to the bottom. Hence the first coefficient of the quotient is the same first coefficient of the dividend.

c) Add terms in vertical patterns and multiply by
`k` in diagonal patterns.

________________________

The solution is shown below. Finally, we can write our solution as:

`(5x^2-22x+8)/(x-4)=5x-2`