Factorise: x^3 + 3x^2 + 3x -7
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Answer: (x-1) is the only real factor.
Step-by-step explanation:
Let p(x)= x^3 + 3x^2 + 3x - 7
p (1) = 1^3 + 3×(1^2) + 3×1 - 7
= 1 + 3 + 3 - 7
= 0
Therefore , (x-1) is a factor of the given polynomial.
Then divide the given polynomial by (x-1) . [by long division]
We get a quadratic polynomial ,
x^2 + 4x + 7
Finding the discriminant of the quadratic polynomial,
b^2 - 4ac = 4^2 - 4×1×7
= 16 - 28
= -12
=> it has no real roots.
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