Question

The partial factorization of x2 – x – 12 is modeled with algebra tiles.Which unit tiles are needed to complete the factorization?

Answer 1

Please write that as x^2 - x - 12 (the "^" symbol denotes exponentiation).

x^2 - x - 12 factors to (x + 3)(x - 4), Check this by multiplication:

x^2 + 3x - 4x - 12 = x^2 - x - 12 (OK).

Answer 2

Answer: The unit of tiles that are needed to complete the factorization are

`(x-4)(x+3)`

Explanation:

Since we have given that

`x^2-x-12=0`

We need to factorise the above quadratic equation:

We use "Split the middle term":

`x^2-x-12=0\\\\x^2-4x+3x-12=0\\\\x(x-4)+3(x-4)=0\\\\(x-4)(x+3)=0`

Hence, the unit of tiles that are needed to complete the factorization are

`(x-4)(x+3)`