What is 2x^2-11x-21 factored using the form ax^2+bx+c?

You can factor the polynomial by first finding a factor pair for "a" times "c" that adds to equal "b".
a = 2
b = -11
c = -21

ac = -42
factor pairs: (21,2) (14,3) (6,7)
-14 + 3 = -11

then the polynomial becomes
2x^2 - 14x + 3x - 21

now group the terms and factor

(2x^2 - 14x) + (3x - 21)
2x(x - 7) + 3(x - 7)

see how after factoring you get the same parenthesis? that means you grouped terms correctly.

since the parenthesis are the same the outer multiples can be combined (like 3x + 4x = (3+4)x )

factored = (2x + 3)(x - 7)