SOLUTION: Find a positive value for k for which the polynomial can be factored. x^2 � kx + 29

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 983376: Find a positive value for k for which the polynomial can be factored. x^2 � kx + 29
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

It must be the sum of two factors of 29, but since 29 is prime...

John

My calculator said it, I believe it, that settles it

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Here are all of the ways to multiply to 29 (using 2 whole numbers only)

1*29 = 29
-1*(-29) = 29

The first factorization 1*29 has the factors add to 1+29 = 30.
The second factorization -1*(-29) has the factors add to -1+(-29) = -30.

So k is either +30 or -30. Because we only want a positive number for k, we have k = 30.

The form is x^2 � kx + 29. If k = 30, then we have x^2 � 30x + 29 factoring to (x - 29)(x - 1)

So the final answer is k = 30