Question

x+3 is a factor of 2x5 + 3x4 + 25x2 - 1 by x + 3.


Select the appropriate response:

True
False

Answer 1

Use the polynomial remainder theorem. It says a polynomial $p(x)$ is divisible by $x-c$ if $p(c)=0$.

We have $p(x)=2x^5+3x^4+25x^2-1$, and

$p(-3)=2(-3)^5+3(-3)^4+25(-3)^2-1=-19\neq0$

So $x+3$ is NOT a factor, and the answer is False.

Answer 2

Answer:

False

Step-by-step explanation:

If x + 3 is a factor, x = -3 should be a root

2(-3)⁵ + 3(-3)⁴ + 25(-3)² - 1

-19

Since the remainder is non-zero, -3 is not a root.

Hence x+3 is not a factor