Question

If (x−1) is a factor of x³−kx²+11x−6, then the value of k is:

O a. 6
O b. 5
O c. -6
O d. 1

Answer 1

Explanation:

I used synthetic division and worked in parts. If x - 1 is a factor of that polynomial, then the ending value has to a value that makes -6 go to 0 which is a 6. That is where I started:

1| 1 -k 11 -6

____________6

1 0

Since synthetic division always begins by bringing down the first value and multiplying it by the number outside, we get this:

1| 1 -k 11 -6

____1________6

1 0

Now we have to think about what number times 1 will give us the 6 that's up under the -6. That's a 6:

1| 1 -k 11 -6

____1________6

1 6 0

Now we have to think about what number added to 11 will give us that 6, which is -5:

1| 1 -k 11 -6

______1___-5___6

1 6 0

Now we contemplate what number times 1 will give us the -5 up under the 11, which is -5:

1| 1 -k 11 -6

______1___-5___6

1 -5 6 0

That means that -k + 1 = -5 and

-k = -6 so

k = 6, choice a