Asked by michelle
use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers:
f(x)=x^4+2x^3-7x^2-8x+12
I am totally lost, please help?
f(x)=x^4+2x^3-7x^2-8x+12
I am totally lost, please help?
Answers
Answered by
Steve
all the rational possibilities are
±1,±2,±3,±4,±6,±12
That's a lot, but it's easy to check the small values. A little synthetic division shows that
f(x) = (x-1)(x^3+3x^2-4x-12)
= (x-1)(x-2)(x^2+5x+6)
= (x-1)(x-2)(x+2)(x+3)
±1,±2,±3,±4,±6,±12
That's a lot, but it's easy to check the small values. A little synthetic division shows that
f(x) = (x-1)(x^3+3x^2-4x-12)
= (x-1)(x-2)(x^2+5x+6)
= (x-1)(x-2)(x+2)(x+3)
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