Respuesta :
Louise wants to factorize completely the given polynomial [tex] 4x^{3}+12x^{2}+5x+15 [/tex]
Grouping first, second terms together and third, fourth terms together
= [tex] 4x^{3}+12x^{2}+5x+15 [/tex]
Taking [tex] 4x^{2} [/tex] common from first and second terms of the given expression and taking 5 common from the third and fourth terms.
=[tex] =4x^{2}(x+3)+5(x+3) [/tex]
Taking (x+3) common from the given expression,
=[tex] =(4x^{2}+5)(x+3) [/tex] is the completely factored form.
