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प्रश्न
Use the Remainder Theorem to factorise the following expression:
2x3 + x2 – 13x + 6
उत्तर
Let f(x) = 2x3 + x2 – 13x + 6
Factors of 6 are ±1, ±2, ±3, ±6
Let x = 2, then
f(2) = 2(2)3 + (2)2 – 13 × 2 + 6
= 16 + 4 – 26 + 6
= 26 – 26
= 0
∵ f(2) = 0
∴ x – 2 is the factor of f(x) ...(By Remainder Theorem)
Dividing f(x) by x – 2, we get
`x – 2")"overline(2x^3 + x^3 – 13x + 6)("2x^2 + 5x – 3`
2x3 – 4x2
– +
5x2 – 13x
5x2 – 10x
– +
–3x + 6
–3x + 6
– +
x
∴ f(x) = (x – 2)(2x2 + 5x – 3)
= (x – 2)(2x2 + 6x – x – 3)
= (x – 2)(2x(x + 3) – 1(x + 3))
= (x – 2)(2x – 1)(x + 3)
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