Question

We want to find the zeros of this polynomial:

p(x) = (x2 + 4x + 3)(x2 – 4)
Plot all the zeros (x-intercepts) of the polynomial in the interactive graph.
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Answer 1

x=-3 x=-1 x=2 x=-2

Explanation:

p(x) = (x^2 + 4x + 3)(x^2 – 4)

Set this equal to zero to find the x intercepts

0 = (x^2 + 4x + 3)(x^2 – 4)

Using the zero product property

(x^2 + 4x + 3) =0 (x^2 – 4) =0

Factor

(x+3)(x+1) =0 (x-2) (x+2)=0

Using the zero product property

x+3 =0 x+1 =0 x-2 =0 x+2 =0

x=-3 x=-1 x=2 x=-2