Question

18) Find factors of x²-x-6​

Answer 1

Answer: (x+2)(x-3)

Step-by-step explanation:

Quadratic functions can all be represented by this model equation: ax² + bx + c.

In this case, a = 1, b = -1, and c = -6

When factoring, the format can be changed like this: (x + h)(x + k)

These two forms are equivalent.

We have: x² - x - 6 = (x + h)(x + k)

b = -1 = h + k

c = -6 = hk

Solving this system of equations, you will get h = 2 and k = -3.

Answer 2

We need to first find the factors of the final term, -6, that add up to the coefficient of the middle term, -1x.

-1 + 6 ≠ -1
1 - 6 ≠ -1
-2 + 3 ≠ -1
2 - 3 = -1

Naturally, as the leading term is x², there will be two binomial terms leading with x. So, if our factors are x, 2, and -3:

`x^2-x-6\\(x+2)(x-3)`

The reason we use those specific factors is that it is inevitable for them to interact with x, so they must add up to the coefficient of the middle term and multiply to the final term.