Question

Check whether p(x) = $x^3$​ + 5$x^2$ + 2x - 5 is a multiple of g(x) = x + 2.

• A. p(x) is a multiple of g(x)
• B. p(x) is not a multiple of g(x)
• C. g(x) is a multiple of p(x)
• D. g(x) is not a multiple of p(x)

Answer 1

The correct option is B

p(x) is not a multiple of g(x)

Consider p(x) = $x^3$​ + 5$x^2$ + $2x-5$

If p(-2) = 0, then g($x$) is a factor of p($x$) which implies p($x$) is a multiple of g($x$)

p(-2) = $-2^3$​ + 5$(-2{)}^2$​ + 2(-2) - 5 = - 8 + 20 - 4 - 5 = 3 ≠ 0

Therefore, p($x$) is not a multiple of g($x$).