To simplify the expression given, \( 5x^3 - 8x^2 + 34x^2 \), we first combine like terms. The \( -8x^2 \) and \( 34x^2 \) can be combined as follows:
\[ -8x^2 + 34x^2 = (34 - 8)x^2 = 26x^2 \]
Therefore, the expression simplifies to:
\[ 5x^3 + 26x^2 \]
Next, we look to factor this expression if possible:
\[ 5x^3 + 26x^2 = x^2(5x + 26) \]
However, it appears the options provided are slightly different and do not reflect this exact factorization. Let's analyze the provided options.
- 5x34−2x2+34x2 - Not in standard form.
- Start Fraction 5 x cubed over 4 End Fraction minus 2 x squared plus Start Fraction 3 over 4 x squared End Fraction - Not equivalent.
- 5x4−2+34x2 - Not correctly formed or equivalent.
- Start Fraction 5 x over 4 End Fraction minus 2 plus Start Fraction 3 over 4 x squared End Fraction - Not correct.
- 5x4+34x2 Start Fraction 5 x over 4 End Fraction plus Start Fraction 3 over 4 x squared End Fraction - This is not correctly arranged.
- 5x54−2x4+34x2 - Not well-formed or equivalent.
Since none of the provided responses match our simplified equivalent \( x^2(5x + 26) \) or even any simple rational form derived from the original expression, it’s likely that the answers provided may have formatting errors or other mistakes.
Please check the options for any errors or misinterpretations. For the expression \( 5x^3 + 26x^2 \), the factors are what we retain after simplification, or it could be written in polynomial form.