Question

5a^3+11a^2+4a-2 {FACTORISE}

Answer 1

5a³ + 11a² + 4a - 2
= 5a³ + 5a² + 6a² + 6a - 2a -2
= 5a²(a + 1) + 6a(a + 1 ) -2(a + 1)
= (a + 1)(5a² + 6a - 2)

hence, (a + 1) and (5a² + 6a - 2) are factors of 5a³ + 11a² + 4a - 2 .

you can also factorize (5a² + 6a - 2)
(5a² + 6a - 2 ) = 0
5a² + 6a = 2
a² + (6/5)a = (2/5)
a² + 2.(6/10)a + (6/10)² = (2/5)+(6/10)²
{a + (6/10)}² = 2/5 + 36/100 = (76)/100
a + 6/10 = ±√76/10
a = -6/10 ±√76/10

hence, factors of (5a² + 6a - 2) are {a+6/10-√76/10} and {a + 6/10 + √76/10}

finally,
5a³ + 11a² +4a - 2 = (a + 1){a+6/10-√76/10}{a+6/10+√76/10}