Factor by grouping.
\[
9 x^{3}-15 x^{2}+6 x-10
\]
\[
9 x^{3}-15 x^{2}+6 x-10=\square
\]

Answer

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Answer

\(\boxed{9x^{3} - 15x^{2} + 6x - 10 = (3x - 5)(3x^{2} + 2)}\)

Steps

Step 1 ：Group the terms in pairs: \( (9x^{3} - 15x^{2}) + (6x - 10) \)

Step 2 ：Factor out the greatest common factor (GCF) from each group: \( 3x^{2}(3x - 5) + 2(3x - 5) \)

Step 3 ：Factor out the common binomial factor from each group: \( (3x - 5)(3x^{2} + 2) \)

Step 4 ：\(\boxed{9x^{3} - 15x^{2} + 6x - 10 = (3x - 5)(3x^{2} + 2)}\)