Question 970032

Please help!! I don't know what I am doing!!

Use the remainder theorem to find the remainder when f(x) is divided by x+4. Then use the factor theorem to determine whether x+4 is a factor of f(x).
f(x)=4x^6-64x^4+x^2-18


Thank you in advance!!
<pre>Divisor of polynomial: x + 4, so x = - 4. 
{{{f(x) = 4x^6 - 64x^4 + x^2 - 18}}}
From remainder theorem, {{{f(- 4) = 4(- 4)^6 - 64(- 4)^4 + (- 4)^2 - 18}}} ----- Substituting - 4 for x to determine remainder
{{{f(- 4) = 4(4096) - 64(256) + 16 - 18}}}
f(- 4) = 16,384 – 16,384 + 16 - 18
f(- 4), or remainder is: {{{highlight_green(- 2)}}}
Since there's a remainder of - 2 when x + 4 is used as a factor, or when x = - 4, then x + 4 is NOT a factor.
Remainder should be 0 (zero) for a polynomial to be considered a factor of another polynomial.