find whether * x + 1 is a factor of x2 + x + 1
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We can also factorize a quadratic polynomial, using quadratic formula…
Method:
(1) : First get the value of x for the above polynomial p(x) = 0
(2) : Then take additive inverse of those values of x.
(3) : Then each value is added to x separately to get its factors.
P(x) = x² + x - 1 = 0
=> x = {-1+ - √(1² + 4)}/2 ( using quadratic formula)
=> x = (-1 +√5)/2 & (-1 -√5)/2
Additive inverse of 1st value = -(-1+√5)/2
=(1-√5)/2
Additive inverse of 2nd value = -(-1-√5)/2
= (1+√5)/2
Hence, factors are..
= x + {(1-√5)/2} & x +{(1+√5)/2}
= (2x +1-√5) /2 & (2x +1 +√5)/2
= (1/4) ( 2x+1-√5) (2x+1+√5)
So, factors are (1/4) (2x+1-√5) (2x+1+√5)
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