Question

The trinomial x2 – 3x – 4 is represented by the model. What are the factors of the trinomial?

Answer 1

x^2 – 3x – 4 = (x - 4)(x +1 )
cause
(x - 4)(x +1 ) = x^2 - 4x + x - 4 = x^2 - 3x - 4

answer
(x - 4)(x +1 ) are factors of x^2 – 3x – 4

Answer 2

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

Explanation:

We have been a trinomial
`x^2-3x-4`. We are asked to find the factors of our given trinomial.

We will use split the middle term to solve our given problem. We need to two number whose sum is
`-3` and whose product is
`-4`. We know such two numbers are
`-4\text{ and }1`.

Split the middle term:

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

Make two groups:

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

Factor out GCF of each group:

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

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

Therefore, factors of our given trinomial are
`(x+1)` and
`(x-4)`.