Question

Add the two polynomials:

(4x^3-2x^2+6)+(4x^3-5x^2+2x-1)






A
4x3−10x2−2x+54x^3-10x^2-2x+54x
3
−10x
2
−2x+5

B
8x3−7x2+2x+58x^3-7x^2+2x+58x
3
−7x
2
+2x+5

C
8x3+2x−58x^3+2x-58x
3
+2x−5

D
4x6−10x4+2x+54x^6-10x^4+2x+54x
6
−10x
4
+2x+5

Answer 1

To add the two polynomials \( (4x^3-2x^2+6) \) and \( (4x^3-5x^2+2x-1) \), we will combine like terms.

1. Start by writing the two polynomials vertically:

\[
\begin{array}{r}
4x^3 - 2x^2 + 6 \\
+ (4x^3 - 5x^2 + 2x - 1) \\
\hline
\end{array}
\]

2. Now, we will add the coefficients of each term:

- For \( x^3 \) terms: \( 4x^3 + 4x^3 = 8x^3 \)
- For \( x^2 \) terms: \( -2x^2 - 5x^2 = -7x^2 \)
- For \( x \) terms: \( 0 + 2x = 2x \)
- For constant terms: \( 6 - 1 = 5 \)

3. Putting it all together, we get:

\[
8x^3 - 7x^2 + 2x + 5
\]

Looking at the provided answer choices, the correct answer is:
**B: \( 8x^3 - 7x^2 + 2x + 5 \)**