How do you use the factor theorem to determine whether x-5 is a factor of $3x^2 + 7x + 40$ ?

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Answer 1 · 2016-01-10T00:49:22

Substitute $x=5$ and see if the result is $0$ .

If $f(x) = 3x^2+7x+40$ then $(x-5)$ is a factor if and only if $f(5) = 0$

We find:

$f(5) = 3*5^2+7*5+40 = 75+35+40 = 150 != 0$

So $(x-5)$ is not a factor.

In fact we can tell that $3x^2+7x+40$ has no factors with Real coefficients, since its discriminant is negative:

$Delta = b^2-4ac = 7^2-(4*3*40) = 49-480 = -431$

How do you use the factor theorem to determine whether x-5 is a factor of 3x^2 + 7x + 403x^2 + 7x + 40?