9514 1404 393
Answer:
p(x) = 3(x -2)^4(x +2) . . . in factored form
p(x) = 3x^5 -18x^4 +24x^3 +48x^2 -144x +96 . . . in standard form
Step-by-step explanation:
When a polynomial has a zero at x=p, it has a factor of (x -p). The exponent of the factor is the multiplicity of the zero. The product of factors can be multiplied by 3 to make the leading coefficient be 3.
p(x) = 3(x -2)^4(x -(-2))
= 3(x^4 +4(-2)x^3 +6(-2)^2x^2 +4(-2)^3x +(-2)^4)·(x +2)
= 3(x^4 -8x^3 +24x^2 -32x +16)(x +2)
= 3(x^5 -6x^4 +8x^3 +16x^2 -48x +32)
p(x) = 3x^5 -18x^4 +24x^3 +48x^2 -144x +96
