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प्रश्न
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
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उत्तर
Let f(x) = 2x3 – x2 – 13x – 6
By hit and trial method
Put x = – 2
f(–2) = 2(–2)3 – (–2)2 – 13(–2) – 6
= – 16 – 4 + 26 – 6
= 0
`\implies` (x + 2) is a factor of f(x)
∴ Dividing f(x) by (x + 2)
`x + 2")"overline(2x^3 - x^2 - 13x - 6)(2x^2 - 5x - 3`
2x3 + 4x2
– –
–5x2 – 13x – 6
–5x2 – 10x
+ +
–3x – 6
–3x – 6
+ +
x
So, 2x3 – x2 – 13x – 6 = (x + 2)(2x2 – 5x – 3)
= (x + 2){2x2 – 6x + x – 3}
= (x + 2){2x (x – 3) + 1(x – 3)}
= (x + 2)(x – 3)(2x + 1)
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