\( 3 x^{2}+25 x-18 \) Which of the following is a factor of the polynomial above? \( x-9 \) \( 3 x+3 \) \( 3 x-2 \) \( 3 x+1 \)
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To find a factor of the polynomial \( 3x^{2} + 25x - 18 \), we can use the factor theorem. We can test the given options by substituting the values of \( x \) that would make each factor equal to zero and seeing if they yield zero when plugged into the polynomial. Testing \( 3x - 2 \), we set \( 3x - 2 = 0 \) leading to \( x = \frac{2}{3} \). Substituting \( \frac{2}{3} \) into the polynomial gives us \( 3\left(\frac{2}{3}\right)^{2} + 25\left(\frac{2}{3}\right) - 18 \), which simplifies to 0. Hence, \( 3x - 2 \) is a factor of the polynomial!