Question

A polynomial expression is written
(-4x^2+9x^3+2x)+(-6x^3+7x-2)
which represents the simplified from of this expression
A. 3x^3-4x^2+9x-2
B. -3x^3-10x^2+4r
C.-6x^3-4x^2+5x-2
D.15x^3-10x^2+11x

Answer 1

To simplify the polynomial expression \((-4x^2 + 9x^3 + 2x) + (-6x^3 + 7x - 2)\), we can combine like terms.

1. First, write down the expression clearly:
\[
(-4x^2 + 9x^3 + 2x) + (-6x^3 + 7x - 2)
\]

2. Remove the parentheses:
\[
-4x^2 + 9x^3 + 2x - 6x^3 + 7x - 2
\]

3. Now, combine the like terms:
- For \(x^3\): \(9x^3 - 6x^3 = 3x^3\)
- For \(x^2\): \(-4x^2\) (no other \(x^2\) terms to combine with)
- For \(x\): \(2x + 7x = 9x\)
- Constant term: \(-2\) (there are no other constant terms)

4. Putting it all together:
\[
3x^3 - 4x^2 + 9x - 2
\]

Now, let's compare this result with the given options:
- A. \(3x^3 - 4x^2 + 9x - 2\)
- B. \(-3x^3 - 10x^2 + 4r\)
- C. \(-6x^3 - 4x^2 + 5x - 2\)
- D. \(15x^3 - 10x^2 + 11x\)

The simplified expression matches option A:

**Answer: A. \(3x^3 - 4x^2 + 9x - 2\)**