Question

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

Answer 1

Answer:

Option A - (x + 1) and (x – 4)

Step-by-step 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 $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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

where a=1, b=-3, c=-4  

Solution is given by

$x=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-4)}}{2(1)}$

$x=\frac{3\pm\sqrt{9+16}}{2}$

$x=\frac{3\pm\sqrt{25}}{2}$

$x=\frac{3\pm5}{2}$

$x=\frac{3+5}{2},\frac{3-5}{2}$

$x=4,-1$

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

Therefore, Option A is correct.

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

Answer 2

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