Question

Given that M(x)=4x^2−8x+17
and L(x)=5−2x^2
, choose the expression that represents L(x)−M(x)
.(1 point)
Responses

−6x^2−8x−22
negative 6 x squared minus 8 x minus 22

−6x2+8x−12
negative 6 x squared plus 8 x minus 12

2x^2+8x+22
2 x squared plus 8 x plus 22

−6x^2+8x+22

Answer 1

To find the expression that represents \( L(x) - M(x) \), we need to evaluate \( L(x) \) and \( M(x) \) first and then subtract them.

Given:

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

Now, we will calculate \( L(x) - M(x) \):

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

Distributing the negative sign:

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

Now, combine like terms:

\[
L(x) - M(x) = 5 - 17 + 8x - 2x^2 - 4x^2
\]
\[
L(x) - M(x) = -12 + 8x - 6x^2
\]

Rearranging it, we get:

\[
L(x) - M(x) = -6x^2 + 8x - 12
\]

Thus, the correct expression representing \( L(x) - M(x) \) is:

\[
\boxed{-6x^2 + 8x - 12}
\]