Question

Given that M(x)=4x
2
−8x+17 and L(x)=5−2x
2
, choose the expression that represents L(x)−M(x).
A. −6x
2
−8x−22
B. 2x
2
+8x+22
C. −6x
2
+8x+22
D. −6x
2
+8x−12

Answer 1

To find the expression that represents \( L(x) - M(x) \), we will subtract \( M(x) \) from \( L(x) \).

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

Now, let's calculate \( L(x) - M(x) \):
\[
L(x) - M(x) = (5 - 2x^2) - (4x^2 - 8x + 17)
\]

Distributing the negative sign in front of \( M(x) \):
\[
= 5 - 2x^2 - 4x^2 + 8x - 17
\]

Now combine like terms:
1. Combine the \( x^2 \) terms: \(-2x^2 - 4x^2 = -6x^2\)
2. The \( x \) term is \( 8x \).
3. Combine the constant terms: \( 5 - 17 = -12 \).

Putting it all together, we have:
\[
L(x) - M(x) = -6x^2 + 8x - 12
\]

Therefore, the expression that represents \( L(x) - M(x) \) is:
\[
\boxed{D. \ -6x^2 + 8x - 12}
\]