Subtract the two polynomials:

Question

Subtract the two polynomials:
(6x^4-3x^2+6)-(3x^3-4x^2-4)

A
6x4−3x3+x2+106x^4-3x^3+x^2+106x 
4
 −3x 
3
 +x 
2
 +10

B
6x4+3x3+7x2−106x^4+3x^3+7x^2-106x 
4
 +3x 
3
 +7x 
2
 −10

C
3x4−7x2+23x^4-7x^2+23x 
4
 −7x 
2
 +2

D
6x4−3x3+x2+26x^4-3x^3+x^2+26x 
4
 −3x 
3
 +x 
2
 +2

GPT-4o mini · Answer

To subtract the two polynomials $ (6x^4 - 3x^2 + 6) - (3x^3 - 4x^2 - 4) $, we need to distribute the negative sign to the second polynomial and then combine like terms. 1. Rewrite the expression: $$ 6x^4 - 3x^2 + 6 - (3x^3 - 4x^2 - 4) $$ 2. Distribute the negative sign: $$ 6x^4 - 3x^2 + 6 - 3x^3 + 4x^2 + 4 $$ 3. Combine like terms: - For $x^4$ terms: $6x^4$ - For $x^3$ terms: $-3x^3$ - For $x^2$ terms: $-3x^2 + 4x^2 = x^2$ - For constant terms: $6 + 4 = 10$ Putting it all together, we have: $$ 6x^4 - 3x^3 + x^2 + 10 $$ The final result is: $$ 6x^4 - 3x^3 + x^2 + 10 $$ Now, looking at the options provided: **A:** $6x^4 - 3x^3 + x^2 + 10$ This matches our result. Therefore, the answer is **.