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प्रश्न
Factorize of the following polynomials:
x3 + 13x2 + 31x − 45 given that x + 9 is a factor
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उत्तर
Let f(x) = x3 + 13x2 + 31x − 45 be the given polynomial.
Therefore (x +9) is a factor of the polynomial f(x).
Now,
`f(x) = x^2(x + 9) + 4x (4x (x+9) -5) (x+ 9)`
`= (x+9){x^2 + 4x - 5}`
` = (x+9){x^2 + 5x - x - 5}`
`= (x+9)(x-1)(x+5)`
Hence ( x - 1),(x + 5) and (x + 9)are the factors of polynomial f(x).
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