Question

If any number k is a solution to a polynomial euqation, then that polynomial must factor into the form (x+k)(some expression). True or False?

Answer 1

I believe this is false, and its kind of a tricky one, remember that a solution to a polynomial will result in the entire expression becoming equal to zero

so (x + k)(some expression) = 0

so if we plug in the hypothetical solution x = k

we get (k + k)(some expression) = 0

which would only be true for k = 0 or the other expression equaling zero

but if we change the operation to subtraction: (x - k)

then any number k will result in a solution, so because of that addition instead of subtraction, the statement is false

Answer 2

thank you so much...pre-calc is kicking my butt.