Answer:
g(x) = 4(x - 1)(x2 + 4)(x + 6)
= 4(x - 1)(x + 2)^2(x + 6)
The roots are:
1, -2, and -6
(x - 1), or 1, has a multiplicity of 4,
(x + 2), or -2, has a multiplicity of 2,
and (x + 6), or -6, has a multiplicity of 1
To determine whether or not they're real zeros, substitute them into the equation.
g(1) = 4(1 - 1)2(1 + 2)(1 + 6)
= 4(0)(3)^2(7)
= 0(9)(7)
= 0
g(-2) = 4(-2 - 1)(-2 + 2)^2(-2 + 6)
= 4(-3)(0)^2(4)
= (-12)(0)(4)
= 0
g(-6) = 4(-6 - 1)(-6 +2)^2(-6 + 6)
= 4(-7)(-4)^2(0)
= (-28)(16)(0)
= 0
Since all of the roots, when substituted into the equation equal 0, they're all real zeros.
(Sorry for this being so long..I hope it helped!)
