Question

Factorise: 4(y^2 - 1)^2 - 15(y^2 - 1 )- 4​

Answer 1

$p(x) = {4({y}^{2}-1)}^{2} -15( {y}^{2} - 1) - 4 \\ let \: \: \: \: \: \: \: ({y}^{2} - 1) = x \\ then \: equation \: becomes \\ = 4 {x}^{2} - 15x - 4 \\ = 4 {x}^{2} - 16x + x - 4 \\ = 4x(x - 4) + 1(x - 4) \\ (4x + 1)(x - 4) \\ hence \\ x = \frac{ - 1}{4 } and \: x = 4 \\ {y}^{2} - 1 = \frac{ - 1}{4 } \\ {y}^{2} = \frac{ - 3}{4} \\ y = \frac{ \sqrt{3} i}{2 } \\ {y}^{2} - 1 = 4 \\ {y}^{2} = 5 \\ y = \sqrt{5}$