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प्रश्न
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
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उत्तर
f(x) = 4x3 + 7x2 – 36x – 63
For x = 3,
f(x) = f(3)
= 4(3)3 + 7(3)2 – 36(3) – 63
= 108 + 63 – 108 – 63
= 0
Hence, (x – 3) is a factor of f(x).
4x2 + 19x + 21
`x – 3")"overline(4x^3 + 7x^2 – 36x - 63)`
4x3 – 12x2
– +
19x2 – 36x – 63
19x2 – 57x
– +
21x – 63
21x – 63
– +
0
∴ 4x3 + 7x2 – 36x – 63 = (x – 3)(4x2 + 19x + 21)
= (x – 3)(4x2 + 12x + 7x + 21)
= (x – 3)[4x(x + 3) + 7(x + 3)]
= (x – 3)(4x + 7)(x + 3)
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