Question

Simon is factoring the polynomial. x2−4x−12 (x−6)(x ______) what value should simon write on the line? −6 −2 2 6

Answer 1

To factor the polynomial x^2-4x-12 using the method of factoring by grouping, we can first find two numbers whose product is -12 and whose sum is -4. These numbers are -6 and 2, because (-6) * (2) = -12 and (-6) + (2) = -4.

Using this information, we can rewrite the polynomial as:

x^2 - 6x + 2x - 12

Next, we can group the first two terms and the last two terms and factor out the common factors:

x(x - 6) + 2(x - 6)

Notice that both terms have a common factor of (x - 6), so we can factor it out:

(x - 6)(x + 2)

Therefore, the factored form of the polynomial x^2-4x-12 is (x-6)(x+2).

So, Simon should write the value -2 on the line.