I don’t know how to solve this problem in simple way of Polynomials chapter of exercise 2.4 of class 9th math. Give me the best answer of this question Factorize:(ii) x3–3×2–9x–5
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Let p(x) = x3–3x2–9x–5
Factors of 5 are ±1 and ±5
By trial method, we find that
p(5) = 0
So, (x-5) is factor of p(x)
Now,
p(x) = x3–3x2–9x–5
p(5) = (5)3–3(5)2–9(5)–5
= 125−75−45−5
= 0
Therefore, (x-5) is the factor of p(x)
Now, Dividend = Divisor × Quotient + Remainder
(x−5)(x2+2x+1) = (x−5)(x2+x+x+1)
= (x−5)(x(x+1)+1(x+1))
= (x−5)(x+1)(x+1)