Question

Factorise: xpower3 - 3xpower2 - 9x - 5

Answer 1

Answer:

$given = factorise \: {x}^{3} - {3x}^{2} - 9x - 5$

By factor theorem:-

let x=-1

$p(x) = {x}^{3} - {3x}^{2} - 9x - 5 = 0$

$p( - 1) = { - 1}^{3} - {3 \times - 1}^{2} - 9 \times - 1 - 5 = 0$

$= - 1 - 3 + 9 - 5 = 0$

$- 9 + 9 = 0$

$0 = 0$

=>(x+1) is a factor of this equation....

$when \:dividsion \: of \: {x}^{3} - {3x}^{2} - 9x - 5 \: by \: (x + 1) \: the \: quotient \: becomes \: {x}^{2} - 4x - - 5 \: and \: remainder \: becomes \: 0$

${x}^{3} - {3x}^{2} - 9x - 5 = (x + 1)( {x}^{2} - 4x - 5)$

splitting the middle term:-

$(x + 1)( {x}^{2} - 5x + x - 5)$

$(x + 1){x(x - 5) + 1(x - 5)}$

$(x + 1)(x + 1)(x - 5) \: are \: the \: zeroes \: of \: the \: polynomial$

THEREFORE, Value of x=-1, 5

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