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प्रश्न
Use factor theorem to factorise the following polynomials completely: x3 – 19x – 30
उत्तर
f(x) = x3 – 19x – 30
Let x = –2, then
f(–2) = (–2)3 – 19(–2) – 30
= –8 + 38 – 30
= 38 – 38
= 0
∴ (x + 2) is a factor of f(x)
Now dividing f(x) by (x + 2), we get
f(x) = x3 – 19x – 30
= (x + 2)(x2 – 2x – 15)
= (x + 2){(x2 –5x + 3x – 15}
= (x + 2){x(x – 5) + 3(x – 5)}
= (x + 2)(x – 5)(x + 3)
`x + 2")"overline(x^3 - 19x - 30)("x^2 - 2x - 15`
x3 + 2x2
– –
–2x2 – 19x
–2x2 – 4x
+ +
–15x – 30
–15x – 30
+ +
x
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