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The Fundamental Theorem of Algebra

Question 3 • [INMT3] Integrated Math 3 Sem 1 (26-27)

Check all of the polynomial functions that have 2 as a root.

Answer
A
h(m) = 8 – m3
B
f(g) = g3 – 2g2 + g
C
f(a) = a3 – 4a2 + a + 6
D
f(x) = x3 – x2 – 4

Explanation

A number is a root of a polynomial when substituting it makes the polynomial equal 0. For A, 8 − 2³ = 8 − 8 = 0; for C, 2³ − 4(2²) + 2 + 6 = 8 − 16 + 2 + 6 = 0; and for D, 2³ − 2² − 4 = 8 − 4 − 4 = 0. Choice B gives 2³ − 2(2²) + 2 = 2, so 2 is not a root of B.

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