Question

Factorise the following polynomials
(x2 – 2x + 3)(x2 – 2x + 5) – 35
(x – 5)2 – (5x – 25) – 24​

Answer 1

Answer:

(y + 2) (y – 3) (y + 8) (y + 3) + 56  

= (y + 2)(y + 3)(y – 3)(y + 8) + 56  

= (y2 + 3y + 2y + 6) (y2 + 8y – 3y – 24) + 56

= (y2 + 5y + 6) (y2 + 5y – 24) + 56

= (m + 6) (m – 24) + 56 … [Putting y2 + 5y = m]  

= m (m – 24) + 6 (m – 24) + 56  

= m2 – 24m + 6m – 144 + 56  = m2 – 18m – 88  

= m2 – 22m + 4m – 88  = m(m – 22) + 4(m – 22)  

= (m – 22) (m + 4)

= (y2 + 5y – 22)(y2 + 5y + 4) … [Replacing m = y2 + 5y]  

= (y2 + 5y – 22) (y2 + 4y + y + 4)  

= (y2 + 5y – 22) [y(y + 4) + 1(y + 4)]

= (y2 + 5y – 22) (y + 4) (y + 1)

ii)    

(x – 5)2 – (5x – 25) – 24  

= (x – 5)2 – (5x – 25) – 24

= (x – 5)2 – 5(x – 5) – 24

= m2 – 5m – 24 … [Putting x – 5 = m]  

= m2 – 8m + 3m – 24

= m(m – 8) + 3(m – 8)

= (m – 8) (m + 3)

= (x – 5 – 8) (x – 5 + 3) … [Replacing m = x – 5]

= (x – 13) (x – 2)