How do you use the factor theorem to determine whether 3x+1 is a factor of $f (x) = 3 x^{4} - 11 x^{3} - 55 x^{2} + 163 x + 60$ $f(x)= 3x^4 -11x^3 - 55x^2 + 163x + 60$ ?

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How do you use the factor theorem to determine whether 3x+1 is a factor of $f (x) = 3 x^{4} - 11 x^{3} - 55 x^{2} + 163 x + 60$ $f(x)= 3x^4 -11x^3 - 55x^2 + 163x + 60$ ?

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Answer 1 · 2018-06-13T02:25:38

$3 x + 1$ $3x+1$ is a factor of $f (x)$ $f(x)$

Explanation:

Let's define $f (c)$ $f(c)$ to be equal to $3 x + 1$ $3x+1$ . Thus, the factor theorem tells us if $f (c) = 0$ $f(c)=0$ , then $3 x + 1$ $3x+1$ is a factor of our polynomial $f (x)$ $f(x)$ .

Let's set $f (c)$ $f(c)$ equal to zero. We get

$3 x + 1 = 0$ $3x+1=0$

$\Rightarrow 3 x = - 1$ $=>3x=-1$

$\Rightarrow x = - \frac{1}{3}$ $=>color(blue)(x=-1/3)$

Now, let's plug this value into our polynomial. This is a hairy problem, so let's not be ashamed to use a calculator. I did but had issues uploading the image, but this evaluates to zero.

Since it evaluated to zero, $3 x + 1$ $3x+1$ is a factor of $f (x)$ $f(x)$ .

Hope this helps!

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How do you use the factor theorem to determine whether 3x+1 is a factor of $f (x) = 3 x^{4} - 11 x^{3} - 55 x^{2} + 163 x + 60$ $f(x)= 3x^4 -11x^3 - 55x^2 + 163x + 60$ ?

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How do you use the factor theorem to determine whether 3x+1 is a factor of f(x)= 3x^4 -11x^3 - 55x^2 + 163x + 60f(x)=3x4−11x3−55x2+163x+60f(x)= 3x^4 -11x^3 - 55x^2 + 163x + 60?

1 Answer

Explanation:

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How do you use the factor theorem to determine whether 3x+1 is a factor of $f (x) = 3 x^{4} - 11 x^{3} - 55 x^{2} + 163 x + 60$ $f(x)= 3x^4 -11x^3 - 55x^2 + 163x + 60$ ?