[tex]a^3-4a^2+12-3a=(a^3-4a^2)-(3a-12)\\\\=a^2(a-4)-3(a-4)=\boxed{(a-4)(a^2-3)}\\\\=(a-4)(a^2-(\sqrt3)^2)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\boxed{(a-4)(a-\sqrt3)(a+\sqrt3)}[/tex]
The factorisation of a³ - 4a² + 12 - 3a is (a - 4)(a² - 3)
a³ - 4a² + 12 - 3a
let's factorise
a³ - 4a² + 12 - 3a
(a³ - 4a²) + (- 3a + 12)
(a³ - 4a²) = (a - 4) • (a²)
(- 3a + 12) = (a - 4) • (-3)
Therefore,
add up the 2 groups
(a - 4)(a² - 3)
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