To check the student's work, let's carefully go through the steps of polynomials subtraction and identify any errors.
The original problem is:
\[ (2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2) \]
Step 1: Distributing the negative sign
When we subtract the second polynomial, we need to distribute the negative sign across all terms in the second polynomial:
\[ 2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2 \]
The student wrote: \[ 2x^3 - 7x^2 + 4x - 9x - 5x^3 + 9x^2 \]
Error Found: In the student's version of Step 1, the term \( -5x^3 \) is written with a negative sign instead of a positive. The correct term should be \( +5x^3 \).
Corrected Step 1:
\[ 2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2 \]
Step 2: Combining like terms
Now, we combine like terms correctly:
- For \(x^3\): \(2x^3 + 5x^3 = 7x^3\)
- For \(x^2\): \(-7x^2 - 9x^2 = -16x^2\)
- For \(x\): \(4x - 9x = -5x\)
So we obtain: \[ 7x^3 - 16x^2 - 5x \]
The student's Step 2 had incorrect calculations due to the error in Step 1.
Final Answer:
The student's final answer was: \[ -3x^3 + 2x^2 - 5x \]
This is incorrect due to the error in Step 1 that led to incorrect combining in Step 2.
Conclusion:
The friend should tell the student that they made an error in Step 1 regarding the sign of the \(5x^3\) term. The correct final answer after properly combining the like terms should be \(7x^3 - 16x^2 - 5x\).
1 answer