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Add the polynomial expressions 2r^2−3r+4

and −2r^2+3r+6

5 answers

To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), you can combine the like terms.

Here are the steps:

  1. Write the polynomials: \[ (2r^2 - 3r + 4) + (-2r^2 + 3r + 6) \]

  2. Group the like terms:

    • Combine the \(r^2\) terms: \(2r^2 - 2r^2\)
    • Combine the \(r\) terms: \(-3r + 3r\)
    • Combine the constant terms: \(4 + 6\)

  3. Perform the addition: \[ 2r^2 - 2r^2 = 0 \] \[ -3r + 3r = 0 \] \[ 4 + 6 = 10 \]

  4. Combine the results: \[ 0 + 0 + 10 = 10 \]

So, the sum of the polynomials \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\) is \(\boxed{10}\).

Expression 1: −3k+4k^3−2


Expression 2: 9k^2−3k^3+4k−3


(2 points)
( )k3+ ( )
k^2+ ( )
k+ ( )

To add the two polynomial expressions and organize the like terms, let's start by rewriting the expressions:

Expression 1: \(-3k + 4k^3 - 2\)

Expression 2: \(9k^2 - 3k^3 + 4k - 3\)

Now, let's combine the polynomials:

  1. Combine the \(k^3\) terms:

    \[ 4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 \quad \text{(or simply } k^3\text{)} \]

  2. Combine the \(k^2\) terms:

    \[ 0 + 9k^2 = 9k^2 \quad \text{(there is no } k^2 \text{ term in Expression 1)} \]

  3. Combine the \(k\) terms:

    \[ -3k + 4k = (4 - 3)k = 1k \quad \text{(or simply } k\text{)} \]

  4. Combine the constant terms:

    \[ -2 - 3 = -5 \]

Now, putting everything together, the result of adding the two expressions is:

\[ 1k^3 + 9k^2 + 1k - 5 \]

Thus, we can fill in the blanks as follows:

\[ (1)k^3 + (9)k^2 + (1)k + (-5) \]

So, to explicitly answer your question:

  • Coefficient of \(k^3\): 1
  • Coefficient of \(k^2\): 9
  • Coefficient of \(k\): 1
  • Constant term: -5

The final answer is:

\[ (1)k^3 + (9)k^2 + (1)k + (-5) \]

Simplify (9x^2−6x+2)−(x^2+4x−39)

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), follow these steps:

  1. Distribute the negative sign across the second polynomial:

\[ 9x^2 - 6x + 2 - x^2 - 4x + 39 \]

  1. Combine like terms:

  • Combine the \(x^2\) terms: \[ 9x^2 - x^2 = 8x^2 \]

  • Combine the \(x\) terms: \[ -6x - 4x = -10x \]

  • Combine the constant terms: \[ 2 + 39 = 41 \]

  1. Put it all together:

\[ 8x^2 - 10x + 41 \]

Thus, the simplified expression is:

\[ \boxed{8x^2 - 10x + 41} \]