Add the polynomial expressions.

Question

Expression #1: 3x^4−2−2x^3+4x

Expression #2: 2x^3−6x−4

(1 point)
Responses

A) 3x^4−2x−6
3 x superscript 4 baseline minus 2 x minus 6

B) 3x^3−4x^2−2x−6
3 x cubed minus 4 x squared minus 2 x minus 6

C) 3x^4−6x−6
3 x superscript 4 baseline minus 6 x minus 6

D) 3x^4−4x^3−2x−6
3 x superscript 4 baseline minus 4 x cubed minus 2 x minus 6

Answer 1

To add the polynomial expressions \(3x^4 - 2 - 2x^3 + 4x\) and \(2x^3 - 6x - 4\), we first need to combine like terms.

Let's rewrite the expressions clearly:

Expression #1:

\[3x^4 - 2 - 2x^3 + 4x\]

Expression #2:

\[2x^3 - 6x - 4\]

Now we can combine them:

1. Combine the \(x^4\) terms:

   • From Expression #1, we have \(3x^4\).
   • (There's no \(x^4\) term in Expression #2, so it remains \(3x^4\).)

2. Combine the \(x^3\) terms:

   • From Expression #1, we have \(-2x^3\).
   • From Expression #2, we have \(+2x^3\).
   • So, \(-2x^3 + 2x^3 = 0\).

3. Combine the \(x\) terms:

   • From Expression #1, we have \(+4x\).
   • From Expression #2, we have \(-6x\).
   • So, \(4x - 6x = -2x\).

4. Combine the constant terms:

   • From Expression #1, we have \(-2\).
   • From Expression #2, we have \(-4\).
   • So, \(-2 - 4 = -6\).

Now we can write the combined polynomial:

\[ 3x^4 + 0 - 2x - 6 \text{ simplifies to } 3x^4 - 2x - 6. \]

So the final result is:

\[ \boxed{A) , 3x^4 - 2x - 6} \]