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

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

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

−6x2+8x−12

Answer 1

To find the expression that represents \( L(x) - M(x) \), we start by substituting the expressions for \( L(x) \) and \( M(x) \):

1. \( M(x) = 4x^2 - 8x + 17 \)
2. \( L(x) = 5 - 2x^2 \)

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

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

Distributing the negative sign:

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

Combine like terms:

• The \( x^2 \) terms: \( -2x^2 - 4x^2 = -6x^2 \)
• The \( x \) terms: \( 8x \) (there's no other \( x \) term to combine with)
• The constant terms: \( 5 - 17 = -12 \)

Putting it all together:

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

Now, we match this expression with the provided options. The correct expression is:

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