Question

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

Select the appropriate response:

True
False

Answer 1

False

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

Answer 2

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\\eq0`

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