Add the polynomial expressions.

Question

Expression #1: 3x4−2−2x3+4x

Expression #2: 2x3−6x−4

(1 point)
Responses

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

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

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

3x3−4x2−2x−6

GPT-4o mini · Answer

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

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

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

Now, let's write them together and combine like terms:

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

Now, combine the like terms:

For \( x^4 \): \( 3x^4 \) (only term)
For \( x^3 \): \( -2x^3 + 2x^3 = 0 \)
For \( x^2 \): \( 0 \) (no \( x^2 \) terms)
For \( x \): \( 4x - 6x = -2x \)
For constant terms: \( -2 - 4 = -6 \)

Putting it all together, we get:

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

Simplifying this gives us:

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

Therefore, the correct response is:

\( 3x^4 - 2x - 6 \).