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9514 1404 393

  factors: (x +5) and (2x -1)

  zeros: -5 and 1/2

Step-by-step explanation:

The factorization can be aided by considering the factors of ac=2·(-5) that have a sum of b=9.

  -10 = -1×10 = -2×5

The sums of these factors are ...

  -1+10 = 9 (the pair we want), and -2+5 = 3

This means we can rewrite the function as ...

  g(x) = 2x² +10x -x -5

and factor by grouping.

  g(x) = (2x² +10x) -(x +5)

  g(x) = 2x(x +5) -1(x +5) = (2x -1)(x +5)

The factors of g(x) are (x +5) and (2x -1).

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The zeros of the function are the values of x that make these factors be zero.

  x+5 = 0   ⇒   x = -5

  2x -1 = 0   ⇒   2x = 1   ⇒   x = 1/2

40 minutes

step-by-step explanation:

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