Question

Imagine you are teaching a younger student how to factor. Describe in full sentences what you would say to teach the young student how to factor the trinomial
`x^(2)` + 4x - 21 into (x - 3)(x + 7). Your description must include at least 3 different steps.

Answer 1

`x^2+ 4x - 21` =(x-3)(x+7)

Explanation:

To factor the trimonial:
`x^2+ 4x - 21`, we follow these steps:

Step 1: Multiply the first and last term

`-21 * x^2=-21x^2`

Step 2: List out product factors of the term derived above

`-21=-1 * 21\\ -21=-3 * 7\\-21=3 * -7\\-21=1 * -21`

Step 3: Determine which of the factors sum up to the middle term 4x

The required product is: -3 and 7

Therefore: -3x+7x=4x

Step 4: Replace the middle term by the expression derived in step 3 and factorize.

`x^2+ 7x -3x- 21\\=x(x+7)-3(x+7)\\=(x-3)(x+7)`