Question

Factorise: 1) x⁴ - 14x² + 1

2) (x² - 2x)² - 23(x² - 2x) +120

Answer 1

x^4 -14x​^2 +1
=x^4 +2x^2 +1-16x^2 [-16+2=-14]
=(x^2 +1)^2 -(4x)^2 [a^2 +2ab+b^2 ]
=(x^2 +1+4x)(x^2 +1-4x) [a^2 -b^2 =(a+b)(a-b)

(x² - 2x)² - 23(x² - 2x) + 120

(x² - 2x) = a

a²-23a + 120

a²-15a – 8a + 120

a(a-15) – 8(a-15)

(a-15)(x-8)

put the value of a

(x² - 2x – 15)( x² - 2x -8)

(x² - 5x + 3x – 15)(x² - 4x + 2x – 8)

[x(x-5) + 3(x-5)] [x(x-4) + 2(x-4)]

(x-5)(x+3)(x-4)(x+2) ans