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)