Question

what is the factorization of $3x^2 - 8x + 5$?
$\bigcirc\\ (3x - 1)(x + 5)$
$\bigcirc\\ (3x + 5)(x - 1)$
$\bigcirc\\ (3x - 1)(x - 5)$
$\bigcirc\\ (3x - 5)(x - 1)$

Explanation:

Step1: Expand each option

For option A: \((3x - 1)(x + 5)=3x^2+15x - x - 5 = 3x^2+14x - 5\)
For option B: \((3x + 5)(x - 1)=3x^2-3x + 5x - 5 = 3x^2+2x - 5\)
For option C: \((3x - 1)(x - 5)=3x^2-15x - x + 5 = 3x^2-16x + 5\)
For option D: \((3x - 5)(x - 1)=3x^2-3x - 5x + 5 = 3x^2-8x + 5\)

Step2: Compare with original expression

The original expression is \(3x^2 - 8x + 5\), which matches the expansion of option D.

Answer:

D. \((3x - 5)(x - 1)\)