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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

1 answer

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. \(3x^3 - 4x^2 + 9x - 2\)