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

Answer 1

To subtract the polynomials \( (6x^4 - 3x^2 + 6) - (3x^3 - 4x^2 - 4) \), we first distribute the negative sign across the second polynomial and then combine like terms.

1. **Rewrite the expression:**
\[
(6x^4 - 3x^2 + 6) - (3x^3 - 4x^2 - 4) = 6x^4 - 3x^2 + 6 - 3x^3 + 4x^2 + 4
\]

2. **Combine like terms:**
- For \(x^4\): \(6x^4\)
- For \(x^3\): \(-3x^3\)
- For \(x^2\): \(-3x^2 + 4x^2 = x^2\)
- For the constant terms: \(6 + 4 = 10\)

3. **Final combined expression:**
\[
6x^4 - 3x^3 + x^2 + 10
\]

Thus, the result of the subtraction is:
\[
6x^4 - 3x^3 + x^2 + 10
\]

This corresponds to option **A**:
\[
\text{A } 6x^4 - 3x^3 + x^2 + 10
\]