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\( 6 x^{2}-19 x+10 \) Select the correct choice below, and if necessary, fill in the answer box to complete your choice. A. \( 6 x^{2}-19 x+10=\square \) B. The trinomial is prime.

Ask by Weston Higgins. in the United States
Mar 19,2025

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\(6x^{2}-19x+10 = (2x-5)(3x-2)\).

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The Deep Dive

To factor \( 6x^{2} - 19x + 10 \), we look for two numbers that multiply to \( 6 \times 10 = 60 \) and add to \( -19 \). Upon inspection, \( -15 \) and \( -4 \) work perfectly since \( -15 + -4 = -19 \) and \( -15 \times -4 = 60\). Thus, we can rewrite the expression as \( 6x^{2} - 15x - 4x + 10 \) and then factor by grouping. This gives us the final factorization of \( (3x - 2)(2x - 5) \). So, the correct choice is A: \( 6 x^{2}-19 x+10=(3x-2)(2x-5) \).

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