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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​

1 answer

To subtract the two polynomials \( (3x^5 - 2x^4 - 5) - (2x^4 + x^2 - 10) \), follow these steps:

  1. Distribute the negative sign through the second polynomial:

\[ = 3x^5 - 2x^4 - 5 - 2x^4 - x^2 + 10 \]

  1. Combine like terms:
  • The \( x^5 \) term: \( 3x^5 \)
  • The \( x^4 \) terms: \( -2x^4 - 2x^4 = -4x^4 \)
  • The \( x^2 \) term: \( -x^2 \)
  • The constant terms: \( -5 + 10 = 5 \)

Putting it all together, we get:

\[ 3x^5 - 4x^4 - x^2 + 5 \]

This expression matches option B:

Answer: B \( 3x^5 - 4x^4 - x^2 + 5 \)