Question

Determine the factors of x^2 − 12x − 20. (5 points)

Answer 1

For this case we must factor the following expression:$x ^ 2-12x-20$

We have that the expression cannot be factored with rational numbers.

On the other hand, we can find the zeros, applying the quadratic formula we have:$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Where:

$a = 1\\b = -12\\c = -20$

$x = \frac {- (- 12) \pm \sqrt {(- 12) ^ 2-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144 + 80}} {2}\\x = \frac {12 \pm \sqrt {224}} {2}\\x = \frac {12 \pm \sqrt {16 * 14}} {2}\\x = \frac {12 \pm4 \sqrt {14}} {2}$

Thus, the roots would be:

$x_ {1} = 6 + 2 \sqrt {14}\\x_ {2} = 6-2 \sqrt {14}$

Answer:

the expression cannot be factored with rational numbers.