The factorisation of the polynomial [tex]2x^3+8x^2+3x+12[/tex] can be done as [tex](2x^2+3)(x+4)[/tex].
A factor of n is a number that when multiplied by another number gives us the number n.
In order to factorise the given polynomial, we need to take the common terms out, therefore, the factorisation of the given polynomial can be done as,
[tex]2x^3+8x^2+3x+12[/tex]
Take 2x² as the common term from the first two terms and 3 from the last two terms,
[tex]2x^3+8x^2+3x+12\\\\= 2x^2(x+4)+3(x+4)\\\\=(2x^2+3)(x+4)[/tex]
Hence, the factorisation of the polynomial [tex]2x^3+8x^2+3x+12[/tex] can be done as [tex](2x^2+3)(x+4)[/tex].
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