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प्रश्न
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
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उत्तर
f(x) = 3x3 + 2x2 – 23x – 30
For x = –2,
f(x) = f(–2)
= 3(–2)3 + 2(–2)2 – 23(–2) – 30
= –24 + 8 + 46 – 30
= –54 + 54
= 0
Hence, (x + 2) is a factor of f(x).
3x2 – 4x – 15
`x + 2")"overline(3x^3 + 2x^2 - 23x - 30)`
3x3 + 6x2
– 4x2 – 23x
– 4x2 – 8x
– 15x – 30
– 15x – 30
0
∴ 3x3 + 2x2 – 23x – 30 = (x + 2)(3x2 – 4x – 15)
= (x + 2)(3x2 + 5x – 9x – 15)
= (x + 2)[x(3x + 5) – 3(3x + 5)]
= (x + 2)(3x + 5)(x – 3)
संबंधित प्रश्न
Check whether 7 + 3x is a factor of 3x3 + 7x.
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Find without division, the remainder in the following:
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When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3)x – 6 leave the same remainder. Find the value of ‘p’.
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).
Check whether p(x) is a multiple of g(x) or not:
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