Question

Factorise: (a 2 -2a) 2 -23(a 2 -2a)+120

Answer 1

P(a) = (a² - 2 a)² - 23 (a² - 2 a) + 120 
        = x² - 23 x + 120
x = a² - 2 a 

120 = 15 * 8           15 + 8 = 23

then   x² - 15 x - 8 x + 120
           (x - 15) x - 8 (x - 15)
           (x - 15) ( x - 8)

so  P(a) = ( a² - 2a -15) (a² - 2a - 8)
              = (a - 5) (a + 3) (a - 4) (a + 2)
by factorizing the two factors.

Answer 2

Answer:P(a) = (a² - 2 a)² - 23 (a² - 2 a) + 120 

        = x² - 23 x + 120

x = a² - 2 a 

120 = 15 * 8           15 + 8 = 23

then   x² - 15 x - 8 x + 120

           (x - 15) x - 8 (x - 15)

           (x - 15) ( x - 8)

so  P(a) = ( a² - 2a -15) (a² - 2a - 8)

              = (a - 5) (a + 3) (a - 4) (a + 2)

by factorizing the two factors.

Step-by-step explanation: