A polynomial of degree 4 with leading coefficient positive 1 has the zeros, x=-3 with multiplicity 2 and x=-1+i. a)Write polynomial in factored form and multiply it out b)Draw sketch

Question

Please answer my question and show me how you got it as soon as you can.

Answer 1

x=-1+i, they come in conjugate pairs, another zero is x=-1-i

x+1 = i

x^2+2x+1 =-1

x^2 +2x +2 = 0

x=-3

x+3 = 0. with multiplicity 2, put an exponent of 2 on the factor x+3

(x+3)^2(x^2+2x+2) = 0

(x^2+6x +9)(x^2+2x+2) = 0

x^4 + 5x^3 + 23x^2 + 30x + 18

the graph has a y intercept of 18, the point (0,18)

the graph never crosses the y axis, but it is tangent to the y axis at x=-3. the graph is otherwise always above the y axis. It's "U" shaped with minimum point at (-3,0). As x approaches + or - infinity, y approaches + infinity.