Question
Subtract the two polynomials:
(3x^5-2x^4-5)-(2x^4+x^2-10)
A
3x5−10x2−5x+103x^{5}-10x^{2}-5x+103x
5
−10x
2
−5x+10
B
3x5−4x4−x2+53x^{5}-4x^{4}-x^{2}+53x
5
−4x
4
−x
2
+5
C
3x5−4x4+x2−153x^{5}-4x^{4}+x^{2}-153x
5
−4x
4
+x
2
−15
D
3x4+x2+153x^{4}+x^{2}+153x
4
+x
2
+15
(3x^5-2x^4-5)-(2x^4+x^2-10)
A
3x5−10x2−5x+103x^{5}-10x^{2}-5x+103x
5
−10x
2
−5x+10
B
3x5−4x4−x2+53x^{5}-4x^{4}-x^{2}+53x
5
−4x
4
−x
2
+5
C
3x5−4x4+x2−153x^{5}-4x^{4}+x^{2}-153x
5
−4x
4
+x
2
−15
D
3x4+x2+153x^{4}+x^{2}+153x
4
+x
2
+15
Answers
GPT-4o mini
To subtract the two polynomials \( (3x^5 - 2x^4 - 5) - (2x^4 + x^2 - 10) \), we first distribute the negative sign to the second polynomial:
\[
3x^5 - 2x^4 - 5 - 2x^4 - x^2 + 10
\]
Next, we combine like terms:
1. \(3x^5\) remains as \(3x^5\).
2. For the \(x^4\) terms: \(-2x^4 - 2x^4 = -4x^4\).
3. For the \(x^2\) term: there is \(-x^2\).
4. The constant terms: \(-5 + 10 = 5\).
Putting it all together, we have:
\[
3x^5 - 4x^4 - x^2 + 5
\]
So, the result of the subtraction is:
\[
3x^5 - 4x^4 - x^2 + 5
\]
Comparing this with the options provided:
- A: \(3x^5 - 10x^2 - 5\)
- B: \(3x^5 - 4x^4 - x^2 + 5\)
- C: \(3x^5 - 4x^4 + x^2 - 15\)
- D: \(3x^4 + x^2 + 15\)
The correct choice is:
**B** \(3x^5 - 4x^4 - x^2 + 5\)
\[
3x^5 - 2x^4 - 5 - 2x^4 - x^2 + 10
\]
Next, we combine like terms:
1. \(3x^5\) remains as \(3x^5\).
2. For the \(x^4\) terms: \(-2x^4 - 2x^4 = -4x^4\).
3. For the \(x^2\) term: there is \(-x^2\).
4. The constant terms: \(-5 + 10 = 5\).
Putting it all together, we have:
\[
3x^5 - 4x^4 - x^2 + 5
\]
So, the result of the subtraction is:
\[
3x^5 - 4x^4 - x^2 + 5
\]
Comparing this with the options provided:
- A: \(3x^5 - 10x^2 - 5\)
- B: \(3x^5 - 4x^4 - x^2 + 5\)
- C: \(3x^5 - 4x^4 + x^2 - 15\)
- D: \(3x^4 + x^2 + 15\)
The correct choice is:
**B** \(3x^5 - 4x^4 - x^2 + 5\)