Question

The trinomial x2 – 3x – 4 is represented by the model.

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

for
`ax^2+bx+c`
if a=1 then we can factor it into (x+r)(x+t) where rt=c and r+t=b

given

`1x^2-3x-4`
what 2 numbers multiply to get -4 and add to get -3?
-4 and 1

(x+1)(x-4)
answer is the first option

Answer 2

Option A - (x + 1) and (x – 4)

Explanation:

Given : The trinomial
`x^2-3x-4` is represented by the model.

To find : What are the factors of the trinomial?

Solution : The given trinomial is a quadratic equation
`y=ax^2+bx+c`

so we solve using by discriminant method.

Solution of x is
`x=(-b\pm√(b^2-4ac))/(2a)`

Comparing with given quadratic equation
`y=x^2-3x-4`

where a=1, b=-3, c=-4

Solution is given by

`x=(-(-3)\pm√((-3)^2-4(1)(-4)))/(2(1))`

`x=(3\pm√(9+16))/(2)`

`x=(3\pm√(25))/(2)`

`x=(3\pm5)/(2)`

`x=(3+5)/(2),(3-5)/(2)`

`x=4,-1`

The factors are (x-4),(x+1)

Therefore, Option A is correct.

The factors of trinomial
`x^2-3x-4=(x-4)(x+1)`