Final answer:
The correct factored form of the quadratic equation 3x²+10x+3 is (x+3)(3x+1).
Step-by-step explanation:
The correct factored form of the quadratic equation 3x²+10x+3 is (x+3)(3x+1).
To find the factored form, we need to factorize the quadratic equation by finding two binomials that multiply together to give us the original equation.
The factored form is found by considering the product of the first terms, the product of the outer terms, the product of the inner terms, and the product of the last terms.
For 3x²+10x+3, the factors are found as follows:
3x²+9x+x+3
New, group the terms:
3x(x+3)+1(x+3)
Notice that (x+3) is a common factor:
(x+3)(3x+1)
We can use the FOIL method to expand (x+3)(3x+1) and verify that it is equal to 3x²+10x+3.