Question

If -2 is a zero of f(x)= xcube+ 13xsq+ 32x+ 20 find it's other zeroes

Answer 1

Hope u like my process
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If - 2 is a zero of f(x) then, (x +2) should be its factors..

Now,

$= > {x}^{3} + 13 {x}^{2} + 32x + 20 = 0 \\ \\ = > {x}^{3} + 2 {x}^{2} + 11 {x}^{2} + 22x + 10x + 20 = 0 \\ \\ = > {x}^{2} (x + 2) + 11x(x + 2) + 10(x + 2) = 0 \\ \\ = > (x + 2)( {x}^{2} + 11x + 10) = 0 \\ \\ = > (x + 2)( {x}^{2} + 10x + x + 10) = 0 \\ \\ = > (x + 2)(x(x + 10) + 1(x + 10)) = 0 \\ \\ = > (x + 2)(x + 1)(x + 10) = 0$
Thus...

The other two zeroes will be - 1, - 10. respectively

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