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Which expression is equivalent to the given trinomial?



(1 point)
Responses

4x(x2+2x+3)
4 x open paren x squared plus 2 x plus 3 close paren

4x(4x+5x)4 x open paren 4 x plus 5 x close paren

(2x2+4)(2x2+3)
open paren 2 x squared plus 4 close paren times open paren 2 x squared plus 3 close paren

(2x2+4)(2x2−3)
open paren 2 x squared plus 4 close paren times open paren 2 x squared minus 3 close paren

1 answer

To determine which expression is equivalent to the given trinomial, let's first analyze the options provided.

  1. 4x(x² + 2x + 3): This expression represents a monomial (4x) multiplied by the trinomial (x² + 2x + 3). When expanded, it becomes 4x³ + 8x² + 12x, which is a cubic polynomial, not a trinomial.

  2. 4x(4x + 5x): This is also a product, where 4x is multiplied by another term (9x). When expanded, it ends up being 36x², which is not a trinomial.

  3. (2x² + 4)(2x² + 3): This is a product of two binomials. When applied, it will yield a polynomial. Specifically, it will generate terms like 4x⁴, 12x² + 8x² + 6, which leads to a fourth-degree polynomial, not a trinomial.

  4. (2x² + 4)(2x² - 3): Like the previous one, this is a product of two binomials. Expanding this will also yield a polynomial rather than a simple trinomial.

From this evaluation, we can see that:

  • Options 1 and 2 do not correspond to a trinomial, as they either lead to a cubic or quadratic expression.
  • Options 3 and 4 would lead to degrees higher than 2.

However, none of these match the characteristics of a trinomial, which typically takes the form of ax² + bx + c.

If a specific trinomial was provided in your question, please clarify it so that I am able to give a correct equivalent expression from your options.