To factor the expression 48x² + 26x + 3, we start by looking for two numbers that multiply to the product of the coefficient of x² (48) and the constant term (3), which is 144, and add up to the coefficient of x (26).
After examining the factors of 144, we find that 18 and 8 work because:
- 18 * 8 = 144
- 18 + 8 = 26
Next, we can rewrite the middle term of the polynomial:
48x² + 18x + 8x + 3
Now we group the terms:
(48x² + 18x) + (8x + 3)
Factor out the common factors in each group:
6x(8x + 3) + 1(8x + 3)
Now, we can factor out the common binomial:
(8x + 3)(6x + 1)
Therefore, the fully factored form of the expression 48x² + 26x + 3 is:
(8x + 3)(6x + 1)