Find ALL values of k so 5x^2 + kx -6 will factor. Show all work please!
Thanks in advance
5x² + kx - 6
5 can only be factored as 5*1, so every possible
factorization must be of this form:
(5x )(x )
Next all the ways to factor 6 are
6*1, 3*2, 2*3 and 1*6
so any possible factorization is in one of
these four forms:
(5x 6)(x 1)
(5x 3)(x 2)
(5x 2)(x 3)
(5x 1)(x 6)
Since the last term of 5x² + kx - 6 is negative
the two signs must be opposite. So we have these
8 possible factorizations, which we multiply out
to find k in each case:
(5x + 6)(x - 1) = 5x² + x - 6 so k = 1
(5x + 3)(x - 2) = 5x² - 7x - 6 so k = -7
(5x + 2)(x - 3) = 5x² - 13x - 6 so k = -13
(5x + 1)(x - 6) = 5x² - 29x - 6 so k = -29
(5x - 6)(x + 1) = 5x² - x - 6 so k = -1
(5x - 3)(x + 2) = 5x² + 7x - 6 so k = 7
(5x - 2)(x + 3) = 5x² + 13x - 6 so k = 13
(5x - 1)(x + 6) = 5x² + 29x - 6 so k = 29
So all possible integer values of k are ±1, ±7, ±13, and ±29.
Edwin
