which polynomial is not a factor of 3x^4-10x^3-29x^2+16x+20?

Question

anonymous · Answer

A)x-1
B)3x+2
C)x+2
D) x-2

I think it is A)

whpalmer4 · Answer

If the polynomial is a factor of the big polynomial, then setting the little polynomial equal to 0 and solving for $x$ will yield a root or zero of the big polynomial.  A zero (or root) has the characteristic that the polynomial's value when evaluated at x = root is identically 0.  So, if x-1 is a factor, x-1=x, x = 1, and $$3(1)^4-10(1)^3-29(1)^2+16(1)+20 = 0$$
If that is true, then $x-1$ is a factor of the polynomial $3x^4-10x^3-29x^2+16x+20$

whpalmer4 · Answer

sorry, that should have been "if x-1 is a factor, x-1=0, x = 1"