Subtract the two polynomials:

Question

(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​

Answer 1

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:

$$=3x^5-2x^4-5-2x^4-x^2+10$$

2. 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 $3x^5-4x^4-x^2+5$