Accuplacer Advanced Algebra and Functions Practice Exam 2025 - Free Advanced Algebra Practice Questions and Study Guide

Question: 1 / 400

Identify the zeros of the polynomial \( f(x) = x^3 - 4x^2 + 5x \).

0, 1, 2

0, 1, 5

To find the zeros of the polynomial \( f(x) = x^3 - 4x^2 + 5x \), we can first factor the polynomial. Observing the polynomial, we notice that there is a common factor of \( x \):

\[

f(x) = x(x^2 - 4x + 5)

\]

Now, we have one zero that can be immediately identified as \( x = 0 \) from the factor \( x \).

Next, we need to find the zeros of the quadratic \( x^2 - 4x + 5 \). To do this, we can apply the quadratic formula, which is given by:

\[

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

\]

In our case, \( a = 1 \), \( b = -4 \), and \( c = 5 \). Plugging in these values, we compute:

\[

x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot 5}}{2 \cdot 1} = \frac{4 \pm \sqrt

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1, 2, 3

2, 3, 4

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