Find the factors of the expression $x^{3} - 5 x^{2} + 8 x - 4$

(x - 1), (x - 2) and (x - 2)

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(x - 1), (x - 2) and (x - 3)

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(x - 4) (x - 1) and (x - 3)

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(x - 9) (x - 2) (x - 3)

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Solution

The correct option is A
(x - 1), (x - 2) and (x - 2)

For x = 1 the value of the given expression

$= (1)^{3} - 5 (1)^{2} + 8 (1) - 4$

9 - 9 = 0

(x - 1) is a factor of $x^{3} - 5 x^{2} + 8 x - 4$

$x^{3} - 5 x^{2} + 8 x - 4$ = (x - 1) $(x^{2} - 4 x + 4)$

= (x - 1) (x - 2) (x - 2)

The factors are (x - 1), (x - 2) and (x - 2)

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Factorize $\sqrt{5}$ $x^{2}$ + 8x + 3 $\sqrt{5}$ = 0 into the form $\sqrt{5}$ $x^{2}$ + px + qx +3 $\sqrt{5}$ = 0.Find the value of p and q.

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