What is the factorization of the expression 48x^2 + 26x + 3?

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To factor the quadratic expression 48x2 + 26x + 3, we first identify the coefficients: a = 48, b = 26, and c = 3. We will use the factoring method where we find two numbers that multiply to a * c = 48 * 3 = 144 and add up to b = 26.

The pair of numbers that meet these criteria are 18 and 8, since 18 * 8 = 144 and 18 + 8 = 26.

Next, we rewrite the middle term using these two numbers:

48x2 + 18x + 8x + 3

Now, we can factor by grouping:

  1. Group the first two terms: (48x2 + 18x)
  2. Group the last two terms: (8x + 3)

Factoring out the common terms from each group gives us:

6x(8x + 3) + 1(8x + 3)

Now, we notice that (8x + 3) is a common factor. We can factor that out:

The factorization is thus:

(8x + 3)(6x + 1)

So, the factorization of the expression 48x2 + 26x + 3 is (8x + 3)(6x + 1).

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