Question

Question 5 (5 points)

(08.03 LC)

Determine the factors of x2 – 8x – 12. (5 points)

(X-6)(x + 2)


(x + 3)(x – 4)


Prime


(x + 6)(x - 2)

Answer 1

The answer is prime.

Explanation:

x2 – 8x – 12

We need two numbers which are factors of 12 such that their product is -12 and their sum is -8. The factors are 1, 2, 3, 4 and 6 but no two numbers satisfy the requirements of summing up to -8 and product of -12.

Therefore the equation is a prime as it has no factor

We can also check if the equation has a factor using the formula for general quadratic equation of ax² + bx + c = 0, the formula is;

(b² - 4ac)

If the answer is a perfect square only then we can factorize the equation.

In the given equation x² - 8x - 12

b = -8 and c = -12

b²- 4ac = (-8)² - 4(1)(-12) = 64 + 48 = 112

Since 112 is not a perfect square number, we can say there is no factors for the given equation.

Answer 2

`(x-9.291)\cdot (x + 1.292)`

Explanation:

The factors of the given polynomial (
`x^(2)-8\cdot x - 12`) are derived from the General Formula for Second-Order Polynomials:

`x = (8 \pm √(64 - 4\cdot (1)\cdot (-12)))/(2\cdot (1))`

`x_(1) \approx 9.291` and
`x_(2) \approx -1.292`

The factors of the polynomial are:

`(x-9.291)\cdot (x + 1.292)`