Final answer:
The given algebraic expression 3a² + 14a + 3 does not simplify to any of the provided options (a, b, c, or d) when using the FOIL method, since none of the pairs result in the matching coefficients, especially for the middle term.
Step-by-step explanation:
To simplify the expression 3a² + 14a + 3, we're looking for two binomials that multiply together to give us this trinomial. We are given four options, so we need to use the FOIL method (First, Outer, Inner, Last) to determine which pair of binomials is correct.
Let's test the options by multiplying the binomials:
- Option a) (3a + 1)(a + 3) = 3a² + 9a + a + 3 = 3a² + 10a + 3
- Option b) (a + 3)(3a + 1) = it's just option a) rearranged and will give the same result.
- Option c) (3a + 3)(a + 1) = 3a² + 3a + 3a + 3 = 3a² + 6a + 3
- Option d) (a + 1)(3a + 3) = it's just option c) rearranged and will give the same result.
Clearly, options a and b provide the correct simplification since they both expand to 3a² + 10a + 3, which differs from the original expression 3a² + 14a + 3 only by the middle term (the coefficient of 'a' is 10 instead of 14). Therefore, none of the given options correctly simplify the original expression.
Upon reviewing the provided options, it is evident that there is perhaps a mistake in the options as none of the options expanded will match the original expression. It is important to double-check solutions and options, and in this case, neither a, b, c, nor d is correct.