Question

find the value of M if X + 4 is a factor of the polynomial X square + 3 X + m

Answer 1

f(x)=x^2+3x+m
g(x)=x+4
zero of g(x)=x=-4
f(-4)=(-4)^2+3(-4)+m=0
16-12+m=0
4+m=0
m=-4


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Answer 2

Answer:

$Value \: of \: m \: = -4$

Step-by-step explanation:

$Let\: p(x)=x^{2}+3x+m$

$If \:(x+4)\: is\:a\:factor\\\: of\: p(x)$

$then\: p(-4)=0$

/* By Factor theorem:

If (x-a) is a factor of p(x) then p(a)=0 */

$(-4)^{2}+3(-4)+m=0$

$\implies16-12+m=0$

$\implies 4+m=0$

$\implies m = -4$

Therefore,

$Value \: of \: m \: = -4$

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