# How do you factor #24r^2 - 10r - 21#?

##### 2 Answers

The discriminant of this quadratic is given by the formula:

Being a positive perfect square, the equation

That is

Hence

Factor f(x) = 24x^2 - 10x - 21 = (x - p)(x - q).

Use the new AC Method to factor trinomials. It is fast, systematic, no factoring, no solving binomials.

Converted trinomial

Find p' and q' by composing factor pairs of a.c = -504. Proceed:... (-14, 16)(-18, 28). This last sum is 10 = -b. Then p' = 18 and q' = -28.

Then,

Factored form:

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