Question

1. error analysis describe and correct the error a student made when subtracting the polynomials. \\((-5x^2 + 2x - 3) - (3x^2 - 2x - 6)\\) \\(-5x^2 + 2x - 3 - 3x^2 - 2x - 6\\) \\(-8x^2 - 9\\)

Explanation:

Step1: Distribute the subtraction

When subtracting the polynomial \((3x^2 - 2x - 6)\), we need to distribute the negative sign to each term inside the parentheses. So \(-(3x^2 - 2x - 6)\) should be \(-3x^2 + 2x + 6\), not \(-3x^2 - 2x - 6\).

Step2: Rewrite the expression correctly

The original expression \((-5x^2 + 2x - 3) - (3x^2 - 2x - 6)\) becomes \(-5x^2 + 2x - 3 - 3x^2 + 2x + 6\) after distributing the negative sign.

Step3: Combine like terms

Combine the \(x^2\) terms: \(-5x^2 - 3x^2 = -8x^2\).
Combine the \(x\) terms: \(2x + 2x = 4x\).
Combine the constant terms: \(-3 + 6 = 3\).
So the correct result is \(-8x^2 + 4x + 3\).

Answer:

The student made an error in distributing the negative sign to the terms inside the second polynomial. The correct result of subtracting the polynomials \((-5x^2 + 2x - 3) - (3x^2 - 2x - 6)\) is \(-8x^2 + 4x + 3\).