The factored form of the quadratic expression 6x² + 11x + 10 can be found by using the method of factoring by grouping or by inspection.
First, we need to look for two numbers that multiply to the product of the coefficient of x² (which is 6) and the constant term (which is 10). This product is 6 * 10 = 60. We also need these two numbers to add up to the coefficient of x (which is 11).
The two numbers that fit these criteria are 5 and 6 because 5 + 6 = 11 and 5 * 6 = 30. However, because we actually need to factor using the leading coefficient, we consider the expression 6x² + 5x + 6x + 10.
Now we can group the terms:
- (6x² + 5x) + (6x + 10)
From the first group, we can factor out x:
- x(6x + 5)
From the second group, we can factor out 2:
- 2(3x + 5)
Now combine these factors:
- (3x + 2)(2x + 5)
Therefore, the factored form of the quadratic expression 6x² + 11x + 10 is: