How do you use the factor theorem to determine whether v+5 is a factor of $v^{4} + 16 v^{3} + 8 v^{2} - 725$ $v^4 + 16v^3 + 8v^2 - 725$ ?

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Answer 1 · 2015-12-22T06:30:57

To find if v+5 is a factor then plug in v=-5 in the given polynomial, if the result obtained is zero, then it is a factor.

If $x - a$ $x-a$ is a factor of the polynomial $P (x)$ $P(x)$ then by factor theorem $P (a) = 0$ $P(a)=0$ .

Our question we have to check if $v + 5$ $v+5$ is a factor of $v^{4} + 16 v^{3} + 8 v^{2} - 725$ $v^4+16v^3+8v^2-725$

${(- 5)}^{4} + 16 {(- 5)}^{3} + 8 {(- 5)}^{2} - 725$ $(-5)^4 + 16(-5)^3 + 8(-5)^2 - 725$

$= 625 - 2000 + 200 - 725$ $=625 -2000 + 200 - 725$

$= - 1900$ $=-1900$

$W e \in f e r t ˆ v + 5 i s \neg a f a c \to r .$ $We infer that v+5 is not a factor.$

How do you use the factor theorem to determine whether v+5 is a factor of v4+16v3+8v2−725v^4 + 16v^3 + 8v^2 - 725?