12
lesson pretestMultiple Choice

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Question 12 • Math 3

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

Answer
A
f of x is equal to open paren x minus 1 close paren times open paren x plus 1 close paren to the 11th power
B
f of x is equal to open paren x plus 2 close paren cubed times open paren x squared minus 7 x plus 3 close paren to the 4th power
C
f of x is equal to open paren x to the 5th power plus 7 x plus 14 close paren to the 6th power
D
f of x is equal to 11 x to the 5th power plus 5 x plus 25

Explanation

The Fundamental Theorem of Algebra says a polynomial has as many complex roots as its degree, counting multiplicity. In choice B, (x + 2)^3 has degree 3, and (x^2 − 7x + 3)^4 has degree 2 × 4 = 8, so the product has degree 3 + 8 = 11. Therefore, choice B, the function (x + 2)^3(x^2 − 7x + 3)^4, has exactly 11 roots.

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