9514 1404 393
Answer:
factors: (x +5) and (2x -1)
zeros: -5 and 1/2
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