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disa [49]
4 years ago
8

Algebra II Question. Please explain your answer.

Mathematics
2 answers:
algol134 years ago
8 0
0 is obviously a solution if you substitute 0 for x 

<span>Test 3 </span>

<span>3 * 3^4 - 3^3 - 27 * 3^2 + 9 * 3 = 0 that 3 is a root. </span>

<span>continue testing the remainder.</span>
inessss [21]4 years ago
3 0
First, we could try to factorize the polynomial. We could group the first and third terms, and the second and fourth term:


\displaystyle{ (3x^4-27x^2)-(x^3-9x)=3x^2(x^2-9)-x(x^2-9)

Now, x(x^2-9) is a common factor:

&#10;\displaystyle{ x(3x-1)(x^2-9).

By the difference of squares formula, our final factorization is :

x(3x-1)(x-3)(x+3).

Here we can see clearly that the roots of f(x) are 0, 1/3, 3, and -3.



Remark: we grouped the terms in pairs as we did, noticing that the ratio of the exponents, and coefficient in each pair was the same. 


Answer: 0, 1/3, 3, and -3.
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See below

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