Given that M(x)=4x2−8x+17

Question

and L(x)=5−2x2
, choose the expression that represents L(x)−M(x)
.(1 point)
Responses

−6x2+8x+22
negative 6 x squared plus 8 x plus 22

2x2+8x+22
2 x squared plus 8 x plus 22

−6x2−8x−22
negative 6 x squared minus 8 x minus 22

−6x2+8x−12

Answer 1

To find \( L(x) - M(x) \), we first need to substitute the expressions for \( L(x) \) and \( M(x) \).

Given: \[ M(x) = 4x^2 - 8x + 17 \] \[ L(x) = 5 - 2x^2 \]

Now, we can compute \( L(x) - M(x) \):

\[ L(x) - M(x) = (5 - 2x^2) - (4x^2 - 8x + 17) \]

Distributing the negative sign: \[ = 5 - 2x^2 - 4x^2 + 8x - 17 \]

Now, combine like terms: \[ = 5 - 17 + 8x - 2x^2 - 4x^2 \] \[ = -12 + 8x - 6x^2 \]

Rearranging gives us: \[ = -6x^2 + 8x - 12 \]

Thus, the expression that represents \( L(x) - M(x) \) is: \[ -6x^2 + 8x - 12 \]

So the correct response from the options provided is: \[ -6x^2 + 8x - 12 \]