To find an expression equivalent to 6x² + 19x + 55, we can use factoring methods.
The expression is a quadratic of the form ax² + bx + c, where a = 6, b = 19, and c = 55. We will look for two numbers that multiply to (a * c) = (6 * 55) = 330 and add to b = 19.
The two numbers that satisfy these conditions are 15 and 4, since 15 * 4 = 60 and 15 + 4 = 19. Now we can rewrite the original expression:
6x² + 15x + 4x + 55
Next, we group the terms:
(6x² + 15x) + (4x + 55)
Now we factor out the common terms from each group:
3x(2x + 5) + 11(2x + 5)
Now we can factor out the common binomial (2x + 5):
(3x + 11)(2x + 5)
Thus, the expression equivalent to 6x² + 19x + 55 is (3x + 11)(2x + 5).