Posted by **Jill** on Tuesday, April 9, 2013 at 2:45pm.

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)=25x^4+26x^3+126x^2+130x+5

Find the real zeros

x=

Use the real zeros to factor f

f(x)=

- rational zeros theorem -
**Reiny**, Tuesday, April 9, 2013 at 2:53pm
only possible rational roots are

x = ±1, ±1/5, ± 1/25

quickly found x=-1 to work

so one factor is x+1

after reducing it to a cubic by synthetic division, it took a bit longer to find x = -1/25 to work

so (25x+1) is another factor

long algebraic divsion gave the last factor as x^2 + 5, which has no real roots.

so real roots are

x = -1 and x = -1/25

- rational zeros theorem -
**Steve**, Tuesday, April 9, 2013 at 3:07pm
just a note:

Things worked out in this case, but x = ±5 were also candidates, since 5/1 has suitable numerator and denominator. For example,

25x^4-100x^3-124x^2-4x-5

has similar coefficients, but has real roots -1 and 5:

(x+1)(x-5)(25x^2+1)

- rational zeros theorem -
**Anonymous**, Friday, April 26, 2013 at 11:46pm
given that f(x) = 9/x-5 and g(x) = 12/x+12 find

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