Question

find the factor of x³+2x²-6x+3

Answer 1

$= {x}^{3} + 2 {x}^{2} - 6x + 3 \\ = {x}^{3} - {x}^{2} + 3{x}^{2} - 3x - 3x + 3 \\ = {x}^{2} (x - 1) + 3x(x - 1) - 3(x - 1) \\ = (x - 1)( {x}^{2} + 3x - 3)$

Answer 2

Answer:

Constant term = 3

Factors of constant term = ± 1 , ± 3

Now putting , x = 1 in x³+2x²-6x+3 = p(x)

p(1) = 1³+2(1)²-6(1)+3

= 1+2-6+3

= 6-6

= 0

=》 p(1) = 0

x = 1 is zero of p(x)

So , (x-1) is a factor of p(x)

___________

Now , x-1 ) x³+2x²-6x+3 ( x²+3x-3

±x³±x²

-----------------------

3x²-6x+3

±3x²±3x

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-3x+3

±3x±3

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0

DIVIDEND = (Divisor × Quotient ) + Remainder

= (x-1)×(x²+3x-3)+0

= (x-1)×(x²+3x-3)

= (x-1)×(x²-3x-x-3)

= (x-1)×[x(x-3) 1(x-3)]

= (x-1)×(x-3)×(x+1)

So , Factors = (x-1)(x+1)(x-3)

HOPE IT HELPS YOU

THANKS