Question

How do you factor the trinomial `x² - 3x - 10`?

Answer 1

To factor trinomials of the form `x^2` + bx + c, find two numbers that multiply to c and that add to b.

Explanation:

`x^2` - 3x - 10

= (x - 5)(x + 2), since -5 • 2 = -10 and -5 + 2 = -3

So, the proper factoring of your expression would be (x - 5)(x + 2).

A few exercises, for practice. At the end, I put a bonus expression where a is greater than 1, so feel free to ask how to factor expressions such as that one.

1. Factor:

a) `x^2` + 11x + 28

b) `x^2` - 16x + 48

c) `x^2` - 19x - 66

d) `3x^2` + 22x + 32

Hopefully my explanations helped

Answer 2

(x + 2)(x - 5)

Explanation:

`y = x^2 - 3x - 10`
Find a pair of numbers, knowing product (c = -10) and sum (b = -3). You don't have to guess.
Compose factor pairs of (-10) then find the pair whose sum is (b) -->
(-1, 10)(-2, 5). This sum is (5 - 2 = 3 = -b). Then the opposite sum
(2, -5) gives the 2 needed numbers: 2 and -5.

Factored form: (x + 2)(x - 5)

NOTE. In case a > 1, to factor a trinomial in standard form ax^2 + bx + c, use the new AC Method (Socratic Search), that shows a systematic way, no guessing, on how to factor a trinomial