Question

A polynomial expression is written in the box. (-4x^2 + 9x^3 + 2x) + (-6x^3 + 7x - 2) Which represents the simplified form of this expression? A) -4x^2 + 3x^3 + 9x - 2. B) 3x^3 + 9x - 2. C) -10x^3 + 16x - 4. D) -10x^3 + 16x - 2.

Answer 1

The simplified form of the given polynomial expression is 3x^3 - 4x^2 + 9x - 2, by combining like terms. This matches option A.

Step-by-step explanation:

The question asks for the simplified form of the polynomial expression (-4x^2 + 9x^3 + 2x) + (-6x^3 + 7x - 2). To simplify the expression, we combine like terms. Here are the steps:

1. Combine the x^3 terms: 9x^3 - 6x^3 = 3x^3.
2. Combine the x^2 terms: There is only one x^2 term, which is -4x^2, so it remains as is.
3. Combine the x terms: 2x + 7x = 9x.
4. Combine the constant terms: There is only one constant term, which is -2, so it remains as is.

Putting it all together, the simplified form of the expression is 3x^3 - 4x^2 + 9x - 2, which matches option A.