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प्रश्न
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
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उत्तर
Let f(x) = x3 – 7x2 + 14x – 8
f(1) = (1)3 – 7(1)2 + 14(1) – 8
= 1 – 7 + 14 – 8
= 0
Hence, (x – 1) is a factor of f(x).
x2 – 6x + 8
`x - 1")"overline(x^3 - 7x^2 + 14 - 8)`
x3 – x2
– 6x2 + 14x
– 6x2 + 6x
8x – 8
8x – 8
0
∴ x3 – 7x2 + 14x – 8 = (x – 1)(x2 – 6x + 8)
= (x – 1)(x2 – 2x – 4x + 8)
= (x – 1)[x(x – 2) – 4(x – 2)]
= (x – 1)(x – 2)(x – 4)
संबंधित प्रश्न
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’.
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Hence factorise the polynomial completely.
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Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
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Factorize completely using factor theorem:
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While factorizing a given polynomial using the remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
- Is the student’s solution correct in stating that (2x + 1) is a factor of the given polynomial?
- Give a valid reason for your answer.
Also, factorize the given polynomial completely.
