If one factor of 2a⁴ - 5a³ + 6a² - 5a + 2 is (a - 1), what is the other factor?
Solution
Correct Answer: Option A
2a⁴ - 5a³ + 6a² - 5a + 2
=2a⁴ - 2a³-3a³+3a ²+3a ²-3a-2a+2
=2a³(a-1)-3a²(a-1)+3a(a-1)-2(a-1)
=(a-1)(2a³-3a²+3a-2)
=(a-1)(2a³-2a²-a²+a+2a-2)
=(a-1){2a²(a-1)-a(a-1)+2(a-1)}
=(a-1)(a-1)(2a²-a+2)
অতেব,অপর উৎপাদকটি =(2a²-a+2)
=2a⁴ - 2a³-3a³+3a ²+3a ²-3a-2a+2
=2a³(a-1)-3a²(a-1)+3a(a-1)-2(a-1)
=(a-1)(2a³-3a²+3a-2)
=(a-1)(2a³-2a²-a²+a+2a-2)
=(a-1){2a²(a-1)-a(a-1)+2(a-1)}
=(a-1)(a-1)(2a²-a+2)
অতেব,অপর উৎপাদকটি =(2a²-a+2)
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