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Question
x3 + 13x2 + 32x + 20
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Solution
Let `f(x) = x^3 + 13x^2 + 32x + 20` be the given polynomial.
Now, putting x= -1,we get
`⇒ f(-1) = (-1)^3 + 13(-1)^2 + 32(-1) + 20`
` = -1 + 13 - 32 + 20 = -33 + 33`
` =0`
Therefore, (x +1)is a factor of polynomial f(x).
Now,
`f(x) = x^2 (x+1)+12x (x+1)+20(x+1)`
` = (x+1){x^2 + 12x + 20}`
` = (x+1){x^2 + 10x + 2x + 20}`
` = (x+1)(x+2)(x + 10)`
Hence
(x +1),(x+2) and (x+10) are the factors of polynomial f(x).
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