Question

Examine whether x+2 is a factor of x^3 + 3x^2 + 5x + 6​

Answer 1

$x + 2 \\ x + 2 = 0 \\ x = - 2$

${x}^{3} + {3x}^{2} + 5x + 6$

$( { - 2})^{3} + 3( { - 2})^{2} + 5( - 2) + 6$

$= - 8 + 12 - 10 + 6$

$= 0$

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Answer 2

SOLUTION:

p(x)=x^3+3x^2+5x+6

g(x)= x+2

x= -2

put x= -2 in p(x)

p(-2)=(-2)^3+3(-2)^2+5(-2)+6

= -8+12-10+6

= 0

Since p(x) is Zero

x+2 is factor of x3+3x+3×2+5x+6

checking:

Let x= -2

q(x)=2x+4

q(-2)=2(-2)+4

=4+4

=0

Since remainder is Zero

x+2 is a factor of 2x+4

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