Question

If Peter has to subtract (x² - 2x - 4) from (x² + 3x + 5), here is his work. Explain what is wrong with Peter's working.

Answer 1

Peter needs to subtract the second polynomial from the first polynomial by changing the signs and combining like terms, resulting in the correct answer: 5x + 9.

Step-by-step explanation:

The student, Peter, is presented with the task of subtracting one polynomial, (x² - 2x - 4), from another, (x² + 3x + 5). To perform the subtraction correctly, Peter needs to subtract each term of the second polynomial from the corresponding term of the first polynomial. The subtraction should be done as follows:

1. Keep the first polynomial as is: (x² + 3x + 5).
2. Change the sign of each term of the second polynomial: (-x² + 2x + 4).
3. Combine like terms: (x² + 3x + 5) - (x² - 2x - 4) becomes x² + 3x + 5 - x² + 2x + 4.
4. Simplify the expression: (3x + 2x) + (5 + 4), resulting in 5x + 9.

Peter's mistake might be in the signs when performing the subtraction or in incorrectly combining like terms.