Find the zeros of the following polynomial functions, with their multiplicities. (a) f(x)= (x +1)(x − 1)(x² +1) (b) g(x) = (x − 4)^3(x − 2)^8 (c) h(x) = (2x − 3)^5 (d) k(x) =(3x +4)^100(x − 17)^4

Answer:a) zeros of the function are x = 1 and, x = -1b) zeros of the function are x = 2 and, x = 4c) zeros of the function are x = [tex]\frac{3}{2}[/tex] d) zeros of the function are x = [tex]\frac{-4}{3}[/tex]  and, x = 17Step-by-step explanation:Zeros of the function are the values of the variable that will lead to the result of the equation being zero.Thus,a) f(x)= (x +1)(x − 1)(x² +1)now,for the (x +1)(x − 1)(x² +1) = 0the condition that must be followed is (x +1) = 0 ..........(1)or(x − 1) = 0 ..........(2)or(x² +1) = 0 ...........(3)considering the equation 1, we have(x +1) = 0orx = -1for(x − 1) = 0 x = 1and,for (x² +1) = 0orx² = -1orx = √(-1)         (neglected as it is a imaginary root)Thus,zeros of the function are x = 1 and, x = -1b) g(x) = (x − 4)³(x − 2)⁸ now,for the (x − 4)³(x − 2)⁸ = 0the condition that must be followed is (x − 4)³ = 0 ..........(1)or(x − 2)⁸ = 0 ..........(2)considering the equation 1, we have(x − 4)³ = 0orx -4 = 0orx = 4and,for (x − 2)⁸ = 0orx - 2 = 0orx = 2        Thus,zeros of the function are x = 2 and, x = 4c) h(x) = (2x − 3)⁵now,for the (2x − 3)⁵ = 0the condition that must be followed is (2x − 3)⁵ = 0 or2x - 3 = 0or2x = 3orx = [tex]\frac{3}{2}[/tex] Thus,zeros of the function are x = [tex]\frac{3}{2}[/tex] d)   k(x) =(3x +4)¹⁰⁰(x − 17)⁴now,for the (3x +4)¹⁰⁰(x − 17)⁴ = 0the condition that must be followed is (3x +4)¹⁰⁰ = 0 ..........(1)or(x − 17)⁴ = 0 ..........(2)considering the equation 1, we have(3x +4)¹⁰⁰ = 0or(3x +4) = 0or3x = -4orx = [tex]\frac{-4}{3}[/tex] and,for (x − 17)⁴ = 0orx - 17 = 0orx = 17        Thus,zeros of the function are x = [tex]\frac{-4}{3}[/tex]  and, x = 17