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
(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
Answers
GPT-4o mini
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 **A**.
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 **A**.