1
Question
Factorise: (x+1)(x+3)(x−4)(x−6)+24 (4 Marks)
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Solution
(x+1)(x+3)(x−4)(x−6)+24
=(x+1)(x−4)(x+3)(x−6)+24
=(x2−4x+x−4)(x2−6x+3x−18)+24
(1 Mark)
=(x2−3x−4)(x2−3x−18)+24
𝐿𝑒𝑡 x2−3x=a
=(a−4)(a−18)+24 (1 Mark)
=a2−18a−4a+72+24
=a2−22a+96
=a2−16a−6a+96
=a(a−16)−6(a−16) (1 Mark)
=(a−16)(a−6)
Now replacing ‘a’ by x2−3x
=x2−3x−16)(x2−3x−6) (1 Mark)
=(x+1)(x−4)(x+3)(x−6)+24
=(x2−4x+x−4)(x2−6x+3x−18)+24
(1 Mark)
=(x2−3x−4)(x2−3x−18)+24
𝐿𝑒𝑡 x2−3x=a
=(a−4)(a−18)+24 (1 Mark)
=a2−18a−4a+72+24
=a2−22a+96
=a2−16a−6a+96
=a(a−16)−6(a−16) (1 Mark)
=(a−16)(a−6)
Now replacing ‘a’ by x2−3x
=x2−3x−16)(x2−3x−6) (1 Mark)
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