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What is the correct factorization for y = 25x^2 - 30x + 5? a. y = (5x + 1)(5x - 5) b. y = 5(5x-1)(x - 1) c. y = (5x - 1)(5x - 5) d. y = (25x - 5)(x + 1)

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The best way to factorize the given quadratic expression 25x^2 - 30x + 5, is to first look for the greatest common factor.

The greatest common factor that can be extracted out of the coefficients 25, -30 and 5 is 5. After factoring out 5, the expression now looks like this:

5*(5x^2 - 6x + 1)

Now, we have a quadratic in the form of ax^2 + bx + c where a =5, b=-6 and c=1. We aim to factorize the quadratic in the form of (px-q)(rx-s).

To do this, we need to find two numbers that add up to be -6, and multiply to be 5, that is, they should satisfy the equation, pr = 5 and q + s = -6.

The numbers that fulfill these requirements are -5 and -1. Therefore, the quadratic can be factorized as (5x-1)(x-1).

Finally, multiplying in 5 that was factored out at the beginning, we have:

y = 5(5x - 1)(x - 1)

So, the correct factorization is option b, y = 5(5x - 1)(x - 1).

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