Find all common zeroes of x³+5x²-9x-45
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x³ + 5x² -9x -45
= x³ -3x² + 8x² -24x + 15x - 45
= x²( x -3) + 8x ( x -3) +15(x -3)
= (x -3) (x² + 8x +15)
= (x -3)(x² +5x +3x +15)
= (x -3)(x +5)(x +3)
hence, three roots of given polynomial are 3 , -5 and -3
= x³ -3x² + 8x² -24x + 15x - 45
= x²( x -3) + 8x ( x -3) +15(x -3)
= (x -3) (x² + 8x +15)
= (x -3)(x² +5x +3x +15)
= (x -3)(x +5)(x +3)
hence, three roots of given polynomial are 3 , -5 and -3
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