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06/07/2021 10:41 am
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Factorize: x3 + 13x2 + 32x + 20
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06/07/2021 10:43 am
Let p(x) = x3+13x2+32x+20
Factors of 20 are ±1, ±2, ±4, ±5, ±10 and ±20
By trial method, we find that
p(-1) = 0
So, (x+1) is factor of p(x)
p(x)= x3+13x2+32x+20
p(-1) = (−1)3+13(−1)2+32(−1)+20
= −1 + 13 − 32 + 20
= 0
Therefore, (x+1) is the factor of p(x)
Dividend = Divisor × Quotient +Remainder
(x+1)(x2+12x+20) = (x+1)(x2+2x+10x+20)
= (x−5)x(x+2)+10(x+2)
= (x−5)(x+2)(x+10)