Factorise x⁴+5x³+9x²+15x+18
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let f(x)= x^4+5x^3+9x^2+15x+18
when f(-2), f(x)=0
so, (x+2) is one of the factors of f(x)
now, x^4+5x^3+9x^2+15x+18
= x^3 (x+2)+3x^2 (x+2)+3x (x+2)+9(x+2)
= (x+2) (x^3+3x^2+3x+9)
= (x+2) (x^2 (x+3)+3 (x+3))
= (x+2) (x+3) (x^2+3)
when f(-2), f(x)=0
so, (x+2) is one of the factors of f(x)
now, x^4+5x^3+9x^2+15x+18
= x^3 (x+2)+3x^2 (x+2)+3x (x+2)+9(x+2)
= (x+2) (x^3+3x^2+3x+9)
= (x+2) (x^2 (x+3)+3 (x+3))
= (x+2) (x+3) (x^2+3)
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