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Factor of $- 6 x^{2} + 31 x - 35$ are?

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x = \frac{3}{2} x = \frac{1}{3}

x = \frac{5}{2} x = \frac{5}{3}

x = \frac{7}{2} x = \frac{5}{3}

x = \frac{9}{2} x = \frac{7}{3}

answer is C.

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Detailed Solution

Began by subtracting a negative one:

{- 6 x}^{2} + 31 x - 35

- 1 ({6 x}^{2} - 31 x + 35)

The middle word can then be divided to fit both terms and provide the same internal expression.

{6 x}^{2} - 21 x - 10 x + 35

3 x (2 x - 7) - 5 (2 x - 7)

You then combine them to produce

(3 x - 5) (2 x - 7)

You will find your calculated form there.
Now, by equating the first term to zero, we obtain

\Rightarrow (3 x - 5) = 0

\Rightarrow 3 x = 5

\Rightarrow x = \frac{5}{3}

Now, by equating the second term to zero, we obtain

\Rightarrow (2 x - 7) = 0

\Rightarrow 2 x = 7

\Rightarrow x = \frac{7}{2}

Consequently, the variables in the equation

{- 6 x}^{2} + 31 x - 35

are

x = \frac{7}{2} x = \frac{5}{3}

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