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Question
Using factor theorem, factorize each of the following polynomials:
x3 + 6x2 + 11x + 6
Solution
Let f(x) = x3 + 6x2 + 11x + 6 be the given polynomial.
Now, put the x =-1we get
`f(-1) = (-1)^3 + 6(-1)^2 + 11(-1) + 6`
` = -1 + 6 -11 + 6`
` = -12 + 12`
` = 0`
Therefore, (x +1)is a factor of f(x).
Now,
`f(x) = x^2 (x+1) + 5x (x +1) + 6 (x+1)`
` = (x +1){x^2 + 5x + 6}`
` = (x+1) {x^2 + 3x + 2x + 6}`
` = (x +1) (x+2)(x+3)`
`f(x) = x^2 (x+1) + 5`
Hence, (x+1)(x+2)(x+3)are the factors of f(x).
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