The given trinomial is,
[tex]x^2+13x+42[/tex]
When we look at the trinomial, there is no number (coefficient) in front of
[tex]x^2[/tex]
so we know that it is a simple trinomial. All you have to do in a simple trinomial is to find two numbers that not only add up to the b term, but multiply to the c term.
Here, b term is 13 and c term is 42
So two numbers that add upto 13 is, 6 and 7, 5 and 8, 11 and 2.
And the c term is 42. So two numbers that when multiplied gives 42 are,
6 and 7.
As this pair also is there in the b term, that is,
[tex]6+7=13;6\times7=42[/tex]
So, we can write, the given trinomial as,
[tex](x+6)(x+7)[/tex]
Thus, option c is the correct answer. SInce x+7
