Question

factorise x^3+x^2-17x+15​

Answer 1

Step-by-step explanation:

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Answer 2

Question -

Factorise - x³+x²-17x+15

Answer -

Let, p(x) = x³+x²-17x+15

Now,

Factors of 15 are-

$\pm1, \: \pm3, \: \pm5, \: and\: \pm15$

By trial and error method,

p(x) = x³+x²-17x+15

Putting p=1 we will get,

p(1)= (1)³+(1)²-17×1+15

p(1)=1+1-17+15

p(1)=17-17

p(1)=0

We find that p(1) =0. So (x-1) is a factor of p(x)

Now,

$= {x}^{3} + {x}^{2} - 17x + 15$

$= {x}^{3} - {x}^{2} + 2 {x}^{2} - 2x - 15x + 15$

$= {x}^{2} (x - 1) + 2x(x - 1) - 15(x - 1)$

Taking (x-1) common,

$= (x - 1)( {x}^{2} + 2x - 15)$

Now x² +2x-15 can be factorised either by splitting the middle term factorisation or by using the factor theorem.

By splitting the middle term, we have

$= {x}^{2} + 2x - 15$

$= {x}^{2} + (5 - 3)x - 15$

$= {x}^{2} + 5x - 3x - 15$

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

By taking (x+5) common,

$= (x + 5)(x + 3)$

So,

${x}^{3} + {x}^{2} - 17x + 15 = \\ (x - 1)(x + 5)(x + 3)$