1.
Which statement about f(x) = 2x2 – 3x - 5 is true?
A The zeros are - and -1, because f(x) = (x + 1)(2x + 5).
2
5
B The zeros are - and 1, because f(x) = (x - 1)(2x + 5).
2
C The zeros are -1 and, because f(x) = (x + 1)(2x-5).
The zeros are 1 and, because f(x) = (x - 1)(2x - 5).

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Answer:

  C.  The zeros are -1 and 5/2, because f(x) = (x + 1)(2x-5).

Step-by-step explanation:

The zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.

The sign of the constant (-5) tells you the product of the constants in the factors must be -5. That is only true for choices B and C.

Additionally, the x-term needs to match the result of multiplying out the factors.

  B.  (x -1)(2x +5) = 2x^2 +3x -5 . . . . . . . . . wrong x-term (not -3x)

  C.  (x +1)(2x -5) = 2x^2 -3x -5 . . . . . . . . . matches the given f(x)

The factors of C are zero when x=-1, x=5/2.

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