When simplified, which expressions produce the trinomial 4x2−20x−24

Question

? Select the TWO that apply.(2 points)
Responses

−4(x2+5x+6)
negative 4 times open paren x squared plus 5 x plus 6 close paren

4(x2−5x−6)
4 times open paren x squared minus 5 x minus 6 close paren

4(x2−20x−24)
4 times open paren x squared minus 20 x minus 24 close paren

4(x−6)(x+1)

Answer 1

To determine which expressions produce the trinomial \( 4x^2 - 20x - 24 \), let’s simplify each expression and see if any of them equal that trinomial.

1. First Expression: \(-4(x^2 + 5x + 6)\)
   Simplifying this: \[ -4(x^2 + 5x + 6) = -4x^2 - 20x - 24 \] This does not match the trinomial since all the signs are opposite.

2. Second Expression: \(4(x^2 - 5x - 6)\)
   Simplifying this: \[ 4(x^2 - 5x - 6) = 4x^2 - 20x - 24 \] This does match the trinomial.

3. Third Expression: \(4(x^2 - 20x - 24)\)
   Simplifying this: \[ 4(x^2 - 20x - 24) = 4x^2 - 80x - 96 \] This does not match the trinomial.

4. Fourth Expression: \(4(x - 6)(x + 1)\)
   First, we need to expand this: \[ 4((x - 6)(x + 1)) = 4(x^2 + x - 6x - 6) = 4(x^2 - 5x - 6) \] And from above, we know: \[ 4(x^2 - 5x - 6) = 4x^2 - 20x - 24 \] This does match the trinomial as well.

Therefore, the two expressions that produce the trinomial \( 4x^2 - 20x - 24 \) are:

• \( 4(x^2 - 5x - 6) \)
• \( 4(x - 6)(x + 1) \)