without actual division show that x cube minus 3 x square - 13 x + 15 is exactly divisible by X square + 2 x minus 3
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g(x)=x²+2x-3
=x²+3x-x-3
=x(x+3)-1(x+3)
=(x-1)(x+3)
f(x)=x³-3x²-13x+15
=x³-x²-2x²+2x-15x+15
=x²(x-1)-2x(x-1)-15(x-1)
=(x-1)(x²-2x-15)
=(x-1){x²-5x+3x-15}
=(x-1){x(x-5)+3(x-5)}
=(x-1)(x+3)(x-5)
Hence, f(x) is completely divisible by g(x)
mahikumarimodi:
how is this done
This is done by middle term factorisation
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