Question

check all the statement(s) that are true about the polynomial function graphed.

• its leading coefficient is positive.
• its leading coefficient is negative.
• it has an odd degree.
• it has an even degree.
• it has exactly two real zeroes.
• it has exactly three real zeroes.
• none of the zeroes have even multiplicity.
• none of the zeroes have odd multiplicity.

Explanation:

Analyze end behavior and leading coefficient

$$
LATEXBLOCK0
$$

Since the ends point in opposite directions, the degree is odd. Since it goes from up-left to down-right, the leading coefficient is negative.

Analyze real zeroes and multiplicity

$$
LATEXBLOCK1
$$

At all three intercepts, the graph crosses directly through the x-axis, meaning all three zeroes have odd multiplicity (multiplicity of 1). Thus, none of the zeroes have even multiplicity.

Answer:

• Its leading coefficient is positive.
• Its leading coefficient is negative. (Correct answer)
• **It has an odd degree.</mcq-option>
• It has an even degree.
• It has exactly two real zeroes.

<mcq-correct>It has exactly three real zeroes. (Correct answer)**

• None of the zeroes have even multiplicity. (Correct answer)
• None of the zeroes have odd multiplicity.