Question

The trinomial x2 – 3x – 4 is represented by the model. An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 10 tiles are in the Product spot in 2 columns with 5 rows: 1 is labeled + x squared, 1 is labeled + x, the 4 tiles below + x squared are labeled negative x, and the 4 tiles below the + x tile are labeled negative. What are the factors of the trinomial? (x + 1) and (x – 4) (x + 4) and (x – 1) (x + 5) and (x – 4) (x + 4) and (x – 5)

Answer 1

(x+1) and (x-4)

Explanation:

Since, factors of an expression is the values which after multiplying together give the same expression.

Given quadratic equation,

`x^2 - 3x - 4`

By the middle term splitting,

`x^2 - (4 - 1)x - 4`

By distributive property,

`x^2 - 4x + x - 4`

`x(x-4)+1(x-4)`

`(x+1)(x-4)`

Since,

`x^2 - 3x - 4=(x+1)(x-4)`

i.e. the factors of
`x^2 - 3x - 4` are (x+1) and (x-4).

Answer 2

For this case we must factor the following expression:

`x ^ 2-3x-4`

We must find two numbers that, when multiplied, result in -4, and when added, result in -3.

These numbers are: -4 and +1

`-4 + 1 = -3\\-4 * (+ 1) = - 4`

So:

`x ^ 2-3x-4 = (x-4) (x + 1)`

Answer:

`(x-4) (x + 1)`

Option A