Question

Can the polynomial in the numerator of the expression x^2-5x+7/x-9 be factored to derive (x − 9) as a factor

Answer 1

Explanation:

We can find out by using synthetic division and the fact that x - 9 Might be a 0. If x = 9 is a 0 of that polynomial, then we will get no remainder when we divide the polynomial by 9:

9 | 1 -5 7

____________

First thing to do is bring down the 1 and multiply it by the 9 and put that product up under the -5:

9 | 1 -5 7

______9____

1

Now add down the column to get:

9 | 1 -5 7

_____9____

1 4

Now multiply 4 by 9 and put that product up under the 7:

9 | 1 -5 7

______9__36

1 4

Now add to see what the remainder is:

9 | 1 -5 7

_______9_36

1 4 R43

we have a remainder of 43. Since it is not a 0, then the polynomial is not evenly divisible by x - 9.

So the answer is No.