How can factoring by grouping be used to express a polynomial as a product of two binomials?

For example, $(ax^3 + bx^2) + (cx + d)$.

For example, $x^2(ax + b) + c(ax + b)$.

For example, $(ax + b)(x^2 + c)$.

ACTIVITY 3

3.1.1 The table in 3.1.2 indicates that we are looking for two integers whose product is 6 and whose sum is 5. For a trinomial in the form $x^2 + bx + c$, the product of the two integers is $c$ and their sum is $b$.
Therefore, the values of $b$ and $c$ in the trinomial are:
$b = \boxed{5}$
$c = \boxed{6}$