To find one of the factors of the quadratic expression 3x² + 10x + 3, we can start by factoring it using the method of grouping or by using the quadratic formula. However, in this case, we will look for factors based on trial and error.
The expression is of the form ax² + bx + c, where a = 3, b = 10, and c = 3. We need to find two numbers that multiply to a * c = 3 * 3 = 9 and add up to b = 10.
The numbers that meet these criteria are 9 and 1 because 9 * 1 = 9 and 9 + 1 = 10. We can now rewrite the equation:
3x² + 9x + 1x + 3
Next, we group the terms:
(3x² + 9x) + (1x + 3)
Now, we factor out the common factors in each group:
3x(x + 3) + 1(x + 3)
We see that (x + 3) is a common factor:
(3x + 1)(x + 3)
Thus, one of the factors of the expression 3x² + 10x + 3 is x + 3. Factoring quadratics like this helps to simplify the expression and find its roots more easily.