Question

examine whether x+2 is a factor of x3+3x2+5x+6 and of 2x+4

Answer 1

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Answer 2

Given:

p(x)= x³ + 3x² + 5x + 6

q(x) = 2x + 4

g(x) = x + 2

To Find:

Examine whether x+2 is a factor of x³+3x²+5x+6 and of 2x+4

Solution:

p(x)=x³ + 3x² + 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 a factor of x³+ 3x² + 5x + 6

Now,

g(x) = x+2

let x = -2

q(x) = 2x + 4

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

       = -4 + 4

       =0

since reminder is zero

x+2 is a factor of 2x+4

Hence, x+2 is a factor of both x³+3x²+5x+6 and 2x+4.