Question

F(x)= 3x^3+8x^2-20x-16. Factorise it

Answer 1

$using \: factor \: theorm \: \\ \\ = \geqslant let \: x = 2 \\ \\ putting \: value \\ \\ = \geqslant f(x) = 3 {x}^{3} + 8 {x}^{2} - 20x - 16 \\ \\ = \geqslant f(2) = 3(2) {}^{3} + 8(2) {}^{2} - 20 \times 2 - 16 \\ \\ = \geqslant f = 24 + 32 - 40 - 16 \\ \\ = \geqslant 0 \: \\ \\ so \: \: x - 2\: \\ it \: is \: the \: factor \: of \: 3 {x}^{3} + 8 {x}^{2} - 20x - 16 \\ \\ = \geqslant dividing \: it$

$by \: dividing \: we \: get \: \\ \\ = \geqslant 3 {x}^{2} + 14x + 8 \\ \\ = \geqslant now \: spriting \: the \: middle \: term \\ \\ = \geqslant 3 {x}^{2} + 14x + 8 \\ \\ = \geqslant spirit \: it \: and \: u \: will \: get \: the \: \\ answer$