check all the statement(s) that are true about the polynomial function graphed. its leading coefficient is…

Explanation:

Step1: Analyze end - behavior

As (x\to-\infty), (y\to-\infty) and as (x\to+\infty), (y\to-\infty). For a polynomial (y = a_nx^n+\cdots+a_0), when the leading coefficient (a_n<0), if (n) is even, (y\to+\infty) as (x\to\pm\infty), and if (n) is odd, (y\to-\infty) as (x\to+\infty) and (y\to+\infty) as (x\to-\infty). Here, since as (x\to+\infty), (y\to-\infty) and as (x\to-\infty), (y\to-\infty), the leading coefficient is negative and the degree is even.

Step2: Count real - zeroes

The graph crosses or touches the (x) - axis at 3 points. So it has exactly three real zeroes.

Step3: Check multiplicity

The graph crosses the (x) - axis at each zero - crossing point. When a graph crosses the (x) - axis at a zero (x = c), the zero has odd multiplicity. So none of the zeroes have even multiplicity.

Answer:

• Its leading coefficient is negative.
• It has an even degree.
• It has exactly three real zeroes.
• None of the zeroes have even multiplicity.