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प्रश्न
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
उत्तर
f(x) = x3 – 13x – 12
Let x = 4, then
f(x) = (4)3 – 13(4) – 12
= 64 – 52 – 12
= 64 – 64
= 0
∵ f(x) = 0
∴ x – 4 is a factor of f(x)
Now, dividing f(x) by (x – 4), we get
f(x) = (x – 4)(x2 + 4x + 3)
= (x – 4)(x2 + 3x + x + 3)
= (x – 4)[x(x + 3) + 1(x + 3)]
= (x – 4)(x + 3)(x + 1)
`x – 4")"overline(x^3 – 13x – 12)("x^2 + 4x + 3`
x3 – 4x2
– +
4x2 – 13x
4x2 – 16x
– +
3x – 12
3x – 12
– +
x
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