math help?

Question

Find two negative values of k for which the given polynomial can be factored

r(squared) - 2r +k

Answer 1

When the polynomial is factored, it will look like this:

(r - a)(r - b)

Expanding gives

r^2 - (a + b)r + ab

So we want to pick a and b such that a + b = -2, but ab is negative. The easiest choices are a = 1, b = -3 and a = 2, b = -4. These give us

r^2 - 2r - 3 = (r - 3)(r + 1)
r^2 - 2r - 8 = (r - 4)(r + 2).

Answer 2

When the polynomial is factored, it will look like this:

(r - a)(r - b)

Expanding gives

r^2 - (a + b)r + ab

So we want to pick a and b such that a + b = -2, but ab is negative. The easiest choices are a = 1, b = -3 and a = 2, b = -4. These give us

r^2 - 2r - 3 = (r - 3)(r + 1)
r^2 - 2r - 8 = (r - 4)(r + 2).

Answer 3

You want to pick two negative values a and b such that:
a + b = -2

For k = -3 we have:
(r + 1)(r - 3) = r^2 - 2r - 3

For k = -8 we have:
(r + 2)(r - 4) = r^2 - 2r - 8

Answer 4

r^2 -2r -3 = (r-3)(r+1) so k=-3
r^2 -2r -8 = (r-4)(r+2) so k=-8