Fill in the blanks. If x = a is a zero of a polynomial function f , then the fol

Question

Fill in the blanks.

If x = a is a zero of a polynomial functionf, then the following three statements are true. (a) x = a is a 1---Select---minimumsolutionx-interceptturning pointy-intercept of the polynomial equation f(x) =0.

(b) 2---Select---(x - a)x = -ax = a-xa(x + a)x-a is a factor of the polynomial f(x).

(c) (a, 0) is a3---Select---minimumy-interceptx-interceptvertexturning point of the graph of f. (a) x = a is a 1---Select---minimumsolutionx-interceptturning pointy-intercept of the polynomial equation f(x) =0.

(b) 2---Select---(x - a)x = -ax = a-xa(x + a)x-a is a factor of the polynomial f(x).

(c) (a, 0) is a3---Select---minimumy-interceptx-interceptvertexturning point of the graph of f.

Explanation / Answer

a) solution b)(x-a) c) x-intercept explanations: a) if the polynomial is F(x)=0, then no matter what x is, the "y"or "f(x)" value is zero. therefore, x=a wouldn't be an interceptbecause the graph of F(x)=0 is a horizontal line on the x-axis. x=a is simply a solution. b) i think this is the remainder theorem. The zero of a function isdefined to be a factor of the polynomial. that is, if a is a zero,then (x-a) must be a factor of the polynomial f(x). c) if x=a is a zero, then that means that when you plug in "a" forx into the function, you get f(x)=0. This would make the point(a,0), which would intercept the x axis at x=a.

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