Factor x(b+c)+3b+3c

$x (b + c) + 3 b + 3 c$

Apply the distributive property.

$x b + x c + 3 b + 3 c$

Rewrite $x b + x c + 3 b + 3 c$ in a factored form.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x b + x c) + 3 b + 3 c$

Factor out the greatest common factor (GCF) from each group.

$x (b + c) + 3 (b + c)$

Factor the polynomial by factoring out the greatest common factor, $b + c$ .

$(b + c) (x + 3)$