We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

Which statements are true about the polynomial function?

f(x)= x^4+ 5x^3 -x^2 -5x

Statements(Choose all that apply)

f(x) divided by (x+5) has a remainder of 0.

f(5)=0

(x-5) is a factor of f(x)

f(x)=0 when x=-5

My answer-- Statements 1, 3, and 4. Am I right? I just need to make sure that my answers are accurate. Please help.

Use rational root theorem to determine the factors.

f(x)=2x^3 + x^2 -8x -4

Factors--(x+2), (x+1), (x-2), (x-4), (2x-1), (x+4), (2x+1), (x-1)

My answer-- (x+2) (x+1) (x-2). Am I right? Once again I just need to make sure, thats all, thanks

Guest Nov 9, 2017

#1**+2 **

1) f(x)= x^{4}+5x^{3}-x^{2}-5x

Statements 1, 3, and 4 are correct. 2 is not because f(5) does not equal 0.

The Rational Root Theorem is:\

Let f(x) be a polynomial with integral coefficients. The only **possible rational zeros** of f(x) are:

\(\frac{p}{q}\)

where p is a divisor of the constant term and q is a divisor of the leading coefficient.

So, fators of the constant on top and factors of the LC on bottom.

\(\frac{\pm1, \pm2, \pm4}{\pm1,\pm2}\)

Now, pair them together.

Divide all of the top factors by 1 first, then 2.

\(\pm1,\pm2,\pm4,\pm \frac{1}{2}, \pm1,\pm2\)

Repeating factors can be dropped so the possible factors are \(\pm1,\pm2,\pm4,\pm \frac{1}{2}\) or \((x+1),(x-1),(x+2),(x-2),(x+4),(x-4),(2x+1),(2x-1)\).

So your possible factors are correct.

To see which ones are factors, I woud graph it.

This graph shows that \((-2,0), (-\frac{1}{2},0), (2,0)\) are the zeros. (Here is the graph: https://www.desmos.com/calculator/fx9umcmzu0)

As factors those are (x+2), (2x+1), and (x-2).

AdamTaurus Nov 9, 2017

#1**+2 **

Best Answer

1) f(x)= x^{4}+5x^{3}-x^{2}-5x

Statements 1, 3, and 4 are correct. 2 is not because f(5) does not equal 0.

The Rational Root Theorem is:\

Let f(x) be a polynomial with integral coefficients. The only **possible rational zeros** of f(x) are:

\(\frac{p}{q}\)

where p is a divisor of the constant term and q is a divisor of the leading coefficient.

So, fators of the constant on top and factors of the LC on bottom.

\(\frac{\pm1, \pm2, \pm4}{\pm1,\pm2}\)

Now, pair them together.

Divide all of the top factors by 1 first, then 2.

\(\pm1,\pm2,\pm4,\pm \frac{1}{2}, \pm1,\pm2\)

Repeating factors can be dropped so the possible factors are \(\pm1,\pm2,\pm4,\pm \frac{1}{2}\) or \((x+1),(x-1),(x+2),(x-2),(x+4),(x-4),(2x+1),(2x-1)\).

So your possible factors are correct.

To see which ones are factors, I woud graph it.

This graph shows that \((-2,0), (-\frac{1}{2},0), (2,0)\) are the zeros. (Here is the graph: https://www.desmos.com/calculator/fx9umcmzu0)

As factors those are (x+2), (2x+1), and (x-2).

AdamTaurus Nov 9, 2017