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Which of the following is a root of the polynomial shown below? Look at the graph of the function and find the solutions.
f(x)=x^3+2x^2-x-2
a.1
b.0
c.3
d.2

Which of the following represents the set of possible rational roots for the polynomial shown below? This question is a review from Algebra 2. Remember that possible rational roots take the form of p/q. Where p is a factor of the constant and q is a factor of the leading coefficient.

2x^3+5x^2-8x-20=0

1) x³ + 2x² - x - 2 2) 2x³ + 5x² - 8x - 20 = 0

x²(x + 2) - (x + 2) x²(2x + 5) - 4(2x + 5) = 0

(x + 2)(x² - 1) (2x + 5)(x² - 4) = 0

(x + 2)(x - 1)(x + 1) x = -5/2, +-2

x = -2, 1, -1 << a is the answer.

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AlonsoDehner AlonsoDehner · Answer 2 · 2019-08-01T11:14:03+02:00

Answer:

Step-by-step explanation:

Given is the polynomials as

1) [tex]f(x) = x^3+2x^2-x-2[/tex]

The graph of this function has x intercepts as

-2, -1 and 0

Since f(x) =0 has solutions equivalent to x intercepts we see that the roots are

-2,-1 and 0

2) Given is a polynomial as

[tex]f(x) = 2x^3+5x^2-8x-20 =0[/tex]

Using rational roots theorem we find that

the roots possible are ±1.±2,±4,±5,±10,±20,±1/2,±5/2

Using remainder theorem we see that

f(2) =f(-2)=0

By using division, we find that the other factor is 2x+5

Hence roots are 2,-2, -2.5