Ask a New Question
Menu

Which of the following is a simplified, equivalent form of the rational expression 5x3−8x2+34x2 ?(1 point) Responses 5x54−2x4+34x2 Start Fraction 5 x superscript 5 baseline over 4 End Fraction minus 2 x superscript 4 baseline plus Start Fraction 3 over 4 x squared End Fraction 5x34−2x2+34x2 Start Fraction 5 x cubed over 4 End Fraction minus 2 x squared plus Start Fraction 3 over 4 x squared End Fraction 5x4+34x2 Start Fraction 5 x over 4 End Fraction plus Start Fraction 3 over 4 x squared End Fraction 5x4−2+34x2

1 answer

To simplify the rational expression \( 5x^3 - 8x^2 + 34x^2 \), we first combine like terms:

  1. Combine the \( x^2 \) terms: \[ -8x^2 + 34x^2 = (34 - 8)x^2 = 26x^2 \]

  2. The expression then simplifies to: \[ 5x^3 + 26x^2 \]

Now, we can factor out the greatest common factor (GCF), which is \( x^2 \): \[ = x^2(5x + 26) \]

Now, let's examine the response options provided to identify which one matches \( x^2(5x + 26) \).

  1. \( \frac{5x^5}{4} - 2x^4 + \frac{3}{4}x^2 \)
  2. \( \frac{5x^3}{4} - 2x^2 + \frac{3}{4}x^2 \)
  3. \( \frac{5x^4}{4} + \frac{3}{4}x^2 \)
  4. \( 5x^4 - 2 + \frac{3}{4}x^2 \)

Since none of these options seem to offer a correct simplification of the original expression: \( 5x^3 + 26x^2 \) or its factored form \( x^2(5x + 26) \).

Please double-check the rational expression you would like to simplify, as it looks like there might be a misunderstanding with the content provided.