Solution:
Given is:
[tex]x^2 + 14x + 40[/tex]
Factor the above polynomial
From given,
[tex]x^2 + 14x + 40[/tex]
[tex]Split\ the\ middle\ term\\\\x^2 + 4x + 10x + 40\\\\Break\:the\:expression\:into\:groups\\\\\left(x^2+4x\right)+\left(10x+40\right)[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\\x(x + 4) + (10x + 40)\\\\\mathrm{Factor\:out\:}10\mathrm{\:from\:}10x+40\mathrm{:\quad }10\left(x+4\right)\\\\x(x + 4) + 10(x + 4)\\\\\mathrm{Factor\:out\:common\:term\:}x+4\\\\\left(x+4\right)\left(x+10\right)[/tex]
Thus, the binomials factor of given is (x + 4) and (x + 10)
