How do you find all the zeros of $f(x)=2x^3+5x^2-2x-5$ ?

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Answer 1 · 2016-08-05T22:10:52

$f(x)$ has zeros: $1$ , $-1$ , $-5/2$

This cubic factors by grouping:

$f(x) = 2x^3+5x^2-2x-5$

$=(2x^3+5x^2)-(2x+5)$

$=x^2(2x+5)-1(2x+5)$

$=(x^2-1)(2x+5)$

$=(x^2-1^2)(2x+5)$

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

Hence zeros: $1$ , $-1$ , $-5/2$

How do you find all the zeros of f(x)=2x^3+5x^2-2x-5f(x)=2x^3+5x^2-2x-5?