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06/07/2021 10:45 am
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Factorize: 2y3 + y2 – 2y – 1
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06/07/2021 10:47 am
Let p(y) = 2y3+y2–2y–1
Factors = 2 × (−1) = -2 are ±1 and ±2
By trial method, we find that
p(1) = 0
So, (y-1) is factor of p(y)
p(y) = 2y3+y2–2y–1
p(1) = 2(1)3+(1)2–2(1)–1
= 2+1−2
= 0
Therefore, (y-1) is the factor of p(y)
Dividend = Divisor × Quotient + Remainder
(y−1)(2y2+3y+1) = (y−1)(2y2+2y+y+1)
= (y−1)(2y(y+1)+1(y+1))
= (y−1)(2y+1)(y+1)