How do I solve this?

Question

(x² - 14x + 49) ÷ (x - 7) 

Answer 1

Solve by long division:

 

Set up as so x-7 then in your division x^2-14x+49

 

Due to long division being hard to show in text I will explain it in steps. Take the x from x-7 and see how many times it goes into x squared. Since it goes into 2 times put a x up top above the division area. So now you take that singular x and multiply into back into the x-7 to get x squared minus 7x beneath the x squared minus 14x don't forget to put the inverse for x squared minus 7x which turns it into -x square plus 7x. Cancels the x squares and add the 7x to the -14x. Get the remainder for that and drop down 49 and repeat process of putting in the x from the from the x-7.

 

At the end you will get your result and it depends on if the remainder is equal to 0. 

Answer 2

Factor the numerator.  Note that

 

x² - 14x + 49 = (x - 7)(x - 7)

 

Therefore,

 

(x² - 14x + 49) / (x - 7) = [(x -7)(x - 7)] / (x - 7) = x - 7

Answer 3

There are two ways you can approach this.

 

1) Use division (long or synthetic)

2) Factor the polynomial and cancel out terms.

 

Since the numerator can be factored into two binomial factors, we can use approach 2.

 

(x - 7)(x - 7) ÷ (x - 7)

 

 

(x - 7) cancel out because (x - 7)÷(x - 7) is 1.  This leaves you with (x - 7).

 

The quotient is (x - 7).