Question

Factorise the following:
(t² - t)(4t² - 4t - 5) - 6

Answer 1

(t² - t)(4t² - 4t - 5) - 6
= (t² - t)[4(t² - t) - 5] - 6
= a[4a - 5] - 6 [Taking (t² - t) = a]
= 4a² - 5a - 6
= 4a² - 8a + 3a - 6
= 4a(a - 2) + 3(a - 2)
= (a - 2)(4a + 3)
= (t² - t - 2)[4(t² - t) + 3]
= (t² - 2t + t - 2)(4t² - 4t + 3)
= [t(t - 2) + 1(t - 2)](4t² - 4t + 3)
= [(t - 2)(t + 1)](4t² - 4t + 3)
= (t + 1)(t - 2)(4t² - 4t + 3).