X^2-10x+24
what is the factor of the binomial of that's trinomial

Trinomial just means three things... x^2 - 10x + 24 is a trinomial... when you factor a trinomial you could get two binomial (   )(   ).  which is the product of two binomials (things with two things) 

If you want to factor Ax^2 + Bx + C when the A is 1.  All you do is find the factors of C when added or subtracted give you B.  So factors of 24 are 1,24 or 2,12, or 3,8 or 4,6 and looking at our factors we see -4 and -6 will give us -10... so thats the factors we use and can now form our two binomials.

(x - 4)(x - 6)