Question

$x {}^{3} + 7x {}^{2} + 16x + 12 = ( \times + 2) {}^{2} (x + 3) {}^$
dau coroana!!!!!

Answer 1

   
[tex]\displaystyle\\ x ^3 + 7x^2 + 16x + 12 = ?\\ ~~~~~7x^2 = 3x^2+4x^2 \\ ~~~~~16x=12x+4x\\\\ x ^3 + 7x^2 + 16x + 12 =\\ =x ^3 + 3x^2+4x^2 + 12x+4x + 12 =\\ =(x ^3 + 3x^2)+(4x^2 + 12x)+(4x + 12) =\\ =x^2(x + 3)+4x(x + 3)+4(x + 3) =\\ =(x+3)(x^2+4x+4)=\\ =(x^2+4x+4)(x+3)=\\ =(x^2+2\cdot x\cdot 2+2^2)(x+3)=\\ =\boxed{\bf (x+2)^2(x+3)} [/tex]