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
Answers
GPT-4o mini
To add the two polynomials \( (4x^3 - 2x^2 + 6) + (4x^3 - 5x^2 + 2x - 1) \), we combine like terms.
1. Combine the \(x^3\) terms:
\[
4x^3 + 4x^3 = 8x^3
\]
2. Combine the \(x^2\) terms:
\[
-2x^2 - 5x^2 = -7x^2
\]
3. Combine the \(x\) terms (only from the second polynomial):
\[
2x \text{ (from the second polynomial)}
\]
4. Combine the constant terms:
\[
6 - 1 = 5
\]
Now, putting it all together, we have:
\[
8x^3 - 7x^2 + 2x + 5
\]
Thus, the sum of the two polynomials is:
\[
8x^3 - 7x^2 + 2x + 5
\]
The correct answer is **B**: \( 8x^3 - 7x^2 + 2x + 5 \).
1. Combine the \(x^3\) terms:
\[
4x^3 + 4x^3 = 8x^3
\]
2. Combine the \(x^2\) terms:
\[
-2x^2 - 5x^2 = -7x^2
\]
3. Combine the \(x\) terms (only from the second polynomial):
\[
2x \text{ (from the second polynomial)}
\]
4. Combine the constant terms:
\[
6 - 1 = 5
\]
Now, putting it all together, we have:
\[
8x^3 - 7x^2 + 2x + 5
\]
Thus, the sum of the two polynomials is:
\[
8x^3 - 7x^2 + 2x + 5
\]
The correct answer is **B**: \( 8x^3 - 7x^2 + 2x + 5 \).