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Which example correctly demonstrates polynomial subtraction?(1 point)

Responses

(2x2+6x+1)−(3x2+3x+9)=x2+3x+8
open paren 2 x squared plus 6 x plus 1 close paren minus open paren 3 x squared plus 3 x plus 9 close paren is equal to x squared plus 3 x plus 8

(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8
open paren 2 x squared plus 6 x plus 1 close paren minus open paren 3 x squared plus 3 x plus 9 close paren is equal to negative x squared plus 3 x minus 8

(2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8
open paren 2 x squared plus 6 x plus 1 close paren minus open paren 3 x squared plus 3 x plus 9 close paren is equal to negative 5 x squared plus 3 x minus 8

(2x2+6x+1)−(3x2+3x+9)=5x2+9x+10

1 answer

To determine which option correctly demonstrates polynomial subtraction, we will calculate the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\) step-by-step.

  1. Distribute the negative sign in the second polynomial: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]

  2. Combine like terms:

    • Combine the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
    • Combine the \(x\) terms: \(6x - 3x = 3x\)
    • Combine the constant terms: \(1 - 9 = -8\)

  3. Putting it all together, we have: \[ -x^2 + 3x - 8 \]

Now, let's compare our result with the provided options:

  • The first option is \(x^2 + 3x + 8\): Incorrect
  • The second option is \(-x^2 + 3x - 8\): Correct
  • The third option is \(-5x^2 + 3x - 8\): Incorrect
  • The fourth option is \(5x^2 + 9x + 10\): Incorrect

Hence, the correct response demonstrating polynomial subtraction is:

(2x²+6x+1)−(3x²+3x+9)=−x²+3x−8.