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Given that 3 is a zero of the polynomial g of x equals x cubed plus x squared-4x-24 express g of x as a product of linear factors?
WaterboyBHS
The Factor Theorem says (x − r) is a factor of a polynomial g(x) if and only if r is a root of g(x). Since 3 is a zero, we know g(x) can be divided by (x-3)
In fact, g(x)=(x-3)(x2 +4x+8)
The (x2 +4x+8) has no real roots, (rational roots theorem tells us this) but we can still write it as a product of linear factors using complex numbers.
Since (x+2-2i)(x+2+2i)=(x2 +4x+8)
we have g(x)=(x-3)(x+2-2i)(x+2+2i) which is a product of linear factor.
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Clouser
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