Given that M(x)=4x

Question

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