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Add the polynomial expressions 2r2−3r+4

and −2r2+3r+6
.(1 point)

11 answers

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

\[ (2r^2 - 3r + 4) + (-2r^2 + 3r + 6) \]

Now, group the like terms:

  1. For \(r^2\) terms: \(2r^2 - 2r^2 = 0\)
  2. For \(r\) terms: \(-3r + 3r = 0\)
  3. For constant terms: \(4 + 6 = 10\)

Putting it all together, we get:

\[ 0 + 0 + 10 = 10 \]

Thus, the result of adding the polynomials is:

\[ \boxed{10} \]

Add the expressions.

Expression 1: −3k+4k3−2


Expression 2: 9k2−3k3+4k−3


(2 points)
k3+
k2+
k+

To add the given expressions, we need to combine like terms from both expressions.

Expression 1: \[ -3k + 4k^3 - 2 \]

Expression 2: \[ 9k^2 - 3k^3 + 4k - 3 \]

Now, let's write them together and group like terms:

\[ (4k^3 - 3k^3) + (9k^2) + (-3k + 4k) + (-2 - 3) \]

Now, let's simplify each group:

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

  2. For \(k^2\) terms: \[ 9k^2 = 9k^2 \]

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

  4. For constant terms: \[ -2 - 3 = -5 \]

Now, combine all these results:

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

So the final expression is:

\[ \boxed{k^3 + 9k^2 + k - 5} \]

To fill in the requested format:

  • \(k^3\) = 1
  • \(k^2\) = 9
  • \(k\) = 1
  • Constant = -5

Thus:

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

Simplify (9x2−6x+2)−(x2+4x−39)
.(1 point)
The difference of the polynomials is
.

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we need to distribute the negative sign across the second polynomial and then combine like terms.

  1. Distribute the negative sign:

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

  1. Now combine like terms:

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

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

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

Putting it all together, the simplified expression is:

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

Therefore, the difference of the polynomials is:

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

Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points)
9x2
+
x + 13
– 2x2
+ 12x
+

x2
+ 5x
+ 2

To correctly fill in the blanks for the polynomial equation that shows the subtraction of the second expression from the first, we start with the two expressions provided.

First Expression: \[ 9x^2 + x + 13 \]

Second Expression: \[ 2x^2 - 12x + (blank\ 1) \ \]

Now we write the subtraction:

\[ (9x^2 + x + 13) - (2x^2 + 12x + (blank\ 1)) \]

Steps to Solve:

  1. Distribute the negative sign: \[ 9x^2 + x + 13 - 2x^2 - 12x - (blank\ 1) \]

  2. Combine like terms:

    • For \(x^2\): \(9x^2 - 2x^2 = 7x^2\)
    • For \(x\): \(x - 12x = -11x\)
    • For constant: \(13 - (blank\ 1)\)

Fill in the Blanks:

So, we need the resulting difference after performing the subtraction \(9x^2 + x + 13 - (2x^2 + 12x + (blank\ 1))\).

From our earlier calculation, after subtraction, we have: \[ 7x^2 - 11x + (13 - (blank\ 1)) \]

We will assume that the constant from the second polynomial is 0 for the blanks to be filled.

If we want to set the resulting constant term to be equal to 2 (as stated in the question), then we should solve the equation: \[ 13 - (blank\ 1) = 2 \ (blank\ 1) = 11 \]

Final polynomial equation filled in:

Putting all the blanks together, we have:

\[ 9x^2 + x + 13 - (2x^2 + 12x + 11) = 7x^2 - 11x + 2 \]

Result

  • The blanks to fill are:
  1. The first blank should represent the constant from the second expression: 11
  2. Confirming the resulting terms from subtraction, the resulting difference from the first polynomial minus the revised second polynomial would give:

Hence, the complete polynomial equation that shows the subtraction is:

\[ 9x^2 + x + 13 - (2x^2 + 12x + 11) = 7x^2 - 11x + 2 \]

Your filled answers will look like this:

  • First Polynomial: \(9x^2\)
  • x: \(x\)
  • 13: \(13\)
  • Subtracted: \(2x^2\)
  • 12x: \(12x\)
  • (Blank for constant): \(11\) (to represent the constant \(+11\))
  • Resulting \(x^2\): \(7x^2\)
  • Resulting \(x\): \(-11x\)
  • Resulting Constant: \(2\)

Thus, the final polynomial equation is: \[ 9x^2 + x + 13 - (2x^2 + 12x + 11) = 7x^2 - 11x + 2 \]

can you just fill in the chart? and show me what I'm supposed to put?

Certainly! Based on the expression you provided, here’s how to fill in the chart:

| | \(9x^2\) | \(+\) | \(x\) | \(+\) | \(13\) | |---|----------|-------|-------|-------|-------| | \(–\) | \(2x^2\) | \(+\) | \(12x\) | \(+\) | \(11\) | | | \(=\) | \(7x^2\) | \(–\) | \(11x\) | \(+\) | \(2\) |

Specifically, you should fill in:

  • For the second expression constant term: 11
  • The resulting difference constant term: 2

So to summarize, your answer for the blanks in the chart should be:

  1. First blank (under constant from the second expression): 11
  2. Second blank (resulting constant): 2

This will complete the chart accordingly!

what about the 3rd blank?

I apologize for the confusion earlier! Let's clarify the entire chart based on your original request for the subtraction of the two expressions and properly identify all the blanks.

Given the expressions:

  1. First Expression: \(9x^2 + x + 13\)
  2. Second Expression: \(2x^2 + 12x + 11\) (where we fill the blank as 11)

You're looking for the final result after performing the subtraction:

\[ (9x^2 + x + 13) - (2x^2 + 12x + 11) \]

Perform the subtraction:

  1. Distributing the negative sign: \[ = 9x^2 + x + 13 - 2x^2 - 12x - 11 \]

  2. Combine like terms:

    • For \(x^2\): \(9x^2 - 2x^2 = 7x^2\)
    • For \(x\): \(x - 12x = -11x\)
    • For constants: \(13 - 11 = 2\)

Fill in the chart:

Here’s how it looks filled out:

| | \(9x^2\) | \(+\) | \(x\) | \(+\) | \(13\) | |---|----------|-------|-------|-------|-------| | \(–\) | \(2x^2\) | \(+\) | \(12x\) | \(+\) | \(11\) | | | \(=\) | \(7x^2\) | \(–\) | \(11x\) | \(+\) | \(2\) |

To summarize all the blanks:

  1. First Blank (the constant in the second expression): 11
  2. Second Blank (the resulting constant): 2
  3. Third Blank (for the changes in \(x\) term): -11

So each of your three blanks can be filled as follows:

  • Second Expression Constant: 11
  • Resulting Constant: 2
  • Coefficient of \(x\) in Resulting Expression: -11

If you have any more questions or need further clarification, feel free to ask!