Question

When x² + 3x – 4 is subtracted from x(x² + 3x – 2), the difference is:

A. x³ + 2x2 – 5x + 4
B. x³ + 2x2 + x - 4
C. -X³ – 2x2 + 5x + 4
D. -x³ + 4x2 + x - 4

Answer 1

The difference when x² + 3x – 4 is subtracted from x(x² + 3x – 2) is x³ + 2x² – 5x + 4, which is option A.

Step-by-step explanation:

The student is asking about simplifying a polynomial expression obtained after subtraction. When x² + 3x – 4 is subtracted from x(x² + 3x – 2), we first need to distribute the x in the second expression and then subtract the first expression from it. The steps for the subtraction are as follows:

• First, distribute the x: x(x²) + x(3x) – x(2) = x³ + 3x² – 2x.
• Now subtract x² + 3x – 4 from the above expression: (x³ + 3x² – 2x) – (x² + 3x – 4) = x³ + 3x² – 2x – x² – 3x + 4.
• Combine like terms: x³ + (3x² – x²) + (–2x – 3x) + 4 = x³ + 2x² – 5x + 4.

The result of the subtraction is x³ + 2x² – 5x + 4, which corresponds to option A.