Question

of your streak!
1 week streak level 2 1/2
what could be the equation of p?
choose 1 answer:
a ( p(x) = (x - 1)(x - 4)^2(2x + 3) )
b ( p(x) = (x - 1)^2(x - 4)(2x + 3) )
c ( p(x) = (x - 1)^2(x - 4)(2x + 3)^2 )
d ( p(x) = (x - 1)(x - 4)(2x + 3)^2 )

Explanation:

Step1: Analyze the graph's behavior at roots

The graph has a "bounce" (touch and turn) at one root, indicating a double root (even multiplicity), and crosses the axis at other roots (odd multiplicity). From the options, we check multiplicities.

Step2: Check each option's multiplicities

• Option A: Root \(x = 4\) has multiplicity 2 (even, bounce), \(x = 1\) and \(x=-\frac{3}{2}\) have multiplicity 1 (odd, cross).
• Option B: Root \(x = 1\) has multiplicity 2 (bounce), but graph shows bounce at \(x = 4\) (from the visual, assuming the graph bounces at \(x = 4\)).
• Option C: Two double roots (\(x = 1\) and \(x=-\frac{3}{2}\)), not matching.
• Option D: Root \(x=-\frac{3}{2}\) has multiplicity 2, not matching the graph's bounce at \(x = 4\).

So the correct equation should have a double root at \(x = 4\) (bounce) and single roots at \(x = 1\) and \(x=-\frac{3}{2}\) (cross), which is Option A.

Answer:

A. \( p(x) = (x - 1)(x - 4)^2(2x + 3) \)