Add the polynomial expressions.

Question

Expression #1: 3x4−2−2x3+4x


Expression #2: 2x3−6x−4


(1 point)
Responses

3x4−4x3−2x−6
3 x superscript 4 baseline minus 4 x cubed minus 2 x minus 6

3x4−6x−6
3 x superscript 4 baseline minus 6 x minus 6

3x3−4x2−2x−6
3 x cubed minus 4 x squared minus 2 x minus 6

3x4−2x−6

Answer 1

To add the polynomial expressions, we can combine like terms from both expressions.

Expression #1: \( 3x^4 - 2 - 2x^3 + 4x \)

Expression #2: \( 2x^3 - 6x - 4 \)

Now we will add the two expressions together:

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

   • There is only one from Expression #1: \( 3x^4 \)

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

   • From Expression #1: \( -2x^3 \)
   • From Expression #2: \( 2x^3 \)
   • Combined: \( -2x^3 + 2x^3 = 0 \)

3. Combine the \( x \) terms:

   • From Expression #1: \( 4x \)
   • From Expression #2: \( -6x \)
   • Combined: \( 4x - 6x = -2x \)

4. Combine the constant terms:

   • From Expression #1: \( -2 \)
   • From Expression #2: \( -4 \)
   • Combined: \( -2 - 4 = -6 \)

Putting it all together, we have:

\[ 3x^4 + 0x^3 - 2x - 6 \]

This simplifies to:

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

Thus, the final result of adding the two polynomial expressions is:

3x^4 - 2x - 6.

So, the correct response is:

3x4−2x−6.