Question

Using factor theorem, factorize each of the following polynomial: x3-6x2+3x+10

Answer 1

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Given :

p(x) = x^3 - 6x^2 +3x + 10

Let's assume that (x+1) is a factor

so,

let x+1 = 0

x = -1

so let's substitute -1 in place of x in p(x).

$p(x) = {x}^{3} - 6 {x}^{2} + 3x + 10 \\ p( -1) = ( - 1 {)}^{3} - 6( - 1 {)}^{2} + 3( - 1) + 10 \\ \: \: \: \: \: \: \: \: \: = - 1 - 6 - 3 + 10 \\ \: \: \: \: \: \: \: \: = - 10 + 10 \\ \: \: \: \: \: \: \: \: = \: \: 0$

Therefore, our assumption is correct

(x+1) is the factor of p(x).

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Hope this is useful...