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Which of the following simplifies to the same expression as 4x^2−3x^2+5x−24 ?(1 point) Responses 4x(x−6) 4 x left parenthesis x minus 6 right parenthesis (x+6)(x−4) left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis (x+8)(x−3) left parenthesis x plus 8 right parenthesis left parenthesis x minus 3 right parenthesis 2(x−12)

6 answers

To determine which of the given expressions simplifies to the same expression as \( 4x^2 - 3x^2 + 5x - 24 \), we first simplify the original expression:

\[ 4x^2 - 3x^2 + 5x - 24 = (4x^2 - 3x^2) + 5x - 24 = 1x^2 + 5x - 24 = x^2 + 5x - 24 \]

Now, we need to check which of the provided options simplifies to \( x^2 + 5x - 24 \).

  1. Option 1: \( 4x(x-6) \)

    \[ 4x(x - 6) = 4x^2 - 24x \]

  2. Option 2: \( (x+6)(x-4) \)

    \[ (x + 6)(x - 4) = x^2 - 4x + 6x - 24 = x^2 + 2x - 24 \]

  3. Option 3: \( (x+8)(x-3) \)

    \[ (x + 8)(x - 3) = x^2 - 3x + 8x - 24 = x^2 + 5x - 24 \]

  4. Option 4: \( 2(x - 12) \)

    \[ 2(x - 12) = 2x - 24 \]

From this simplification, we can see that Option 3: \( (x + 8)(x - 3) \) simplifies to \( x^2 + 5x - 24 \), which matches the expression we simplified from the original statement.

So, the correct answer is: (x + 8)(x - 3).

Add the polynomial expressions 5z−2z^2−4z+5 and 6z^2+3−7z .(1 point)

9z^2-11z+8
4z^2-6z+8
4z^2-z+8
11z^2+z-2

To add the polynomial expressions \(5z - 2z^2 - 4z + 5\) and \(6z^2 + 3 - 7z\), we first combine like terms in each expression.

Step 1: Simplify the first polynomial

Starting with the first polynomial: \[ 5z - 2z^2 - 4z + 5 \] Combine the like terms \(5z\) and \(-4z\): \[ (5z - 4z) - 2z^2 + 5 = z - 2z^2 + 5 \] Rearranging gives: \[ -2z^2 + z + 5 \]

Step 2: Rewrite the second polynomial

Now the second polynomial: \[ 6z^2 + 3 - 7z \] Rearranging gives: \[ 6z^2 - 7z + 3 \]

Step 3: Add the two polynomials

Now, add the two simplified polynomials: \[ (-2z^2 + z + 5) + (6z^2 - 7z + 3) \]

Combine like terms:

  • For \(z^2\): \(-2z^2 + 6z^2 = 4z^2\)
  • For \(z\): \(z - 7z = -6z\)
  • For the constant: \(5 + 3 = 8\)

Putting it all together, we get: \[ 4z^2 - 6z + 8 \]

Conclusion

The answer is: \[ \boxed{4z^2 - 6z + 8} \]

Which of the following correctly simplifies (9x^2+17x+13)−(2x^2+12x+11) ?(1 point)
7x^2+5x+2
9x^2+17x+13−2x^2−12x−11
7x^2+29x+24
12x^2+2

To simplify the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\), we can follow these steps:

Step 1: Distribute the negative sign

Distributing the negative sign to each term in the second polynomial gives: \[ (9x^2 + 17x + 13) - 2x^2 - 12x - 11 \]

Step 2: Combine like terms

Now, we can combine the like terms:

  1. For the \(x^2\) terms: \[ 9x^2 - 2x^2 = 7x^2 \]

  2. For the \(x\) terms: \[ 17x - 12x = 5x \]

  3. For the constant terms: \[ 13 - 11 = 2 \]

Step 3: Write the result

Putting it all together, we get: \[ 7x^2 + 5x + 2 \]

Conclusion

Thus, the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\) simplifies to: \[ \boxed{7x^2 + 5x + 2} \]

Multiply the polynomials (3x−1)(2x+4) .(2 points)

()x^2+()x+()