Key to "Factorise x2-2x-8"

Luis Wolf

Answered question

2023-01-28

Factorise

x^{2} - 2 x - 8

rocairasen

Beginner2023-01-29Added 7 answers

The given quadratic equation's factors must be found in factories

x^{2} - 2 x - 8

Let us assume that the equation is in the form

a x^{2} + b x + c

We know that if

α

and

β

are the two root of the quadratic equation

a x^{2} + b x + c

, then

α + β = - \frac{b}{a}

and

α β = \frac{c}{a}

.
In such case the quadratic equation can be expressed as

(x - α) (x - β)

Now comparing the above equation we get

α + β = 2

and

α β = - 8

.
On solving this we get

α = 4

and

β = - 2

.
Thus, the above quadratic expression can be expressed as:

x^{2} - 2 x - 8 = x^{2} - 4 x + 2 x - 8 = x (x - 4) + 2 (x - 4) = (x - 4) (x + 2)

Thus,

(x - 4)

and

(x + 2)

are the factors of the polynomial

x^{2} - 2 x - 8

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