Find the value(s) of k that makes the second polynomial a factor of the first. k^2x^4 + 2kx^2 − 48; x − 1

Answer 1

First polynomial

k²x⁴ + 2kx² - 48

= k²x⁴ + 8kx² - 6kx² - 48

= kx²(kx² + 8) - 6(kx² + 8)

= (kx² + 8) (kx² - 6)

Now, if k = 6, the first polynomial becomes (6x² + 8) (6x² - 6) = (6x² + 8) 6(x² - 1) = (6x² + 8) 6(x + 1)(x - 1)

Again, if k = -8, the first polynomial becomes (-8x² + 8) (-8x² - 6) = (8x² - 8) (8x² + 6) = 8(x² - 1) (8x² + 6) = 8(x + 1)(x - 1) (8x² + 6)

Therefore, the possible values of k are 6 and -8.