Question 23 • CMS 2026-2027 NC Math 3 CREDIT RECOVERY
A polynomial function has a root of negative 3 with multiplicity 2 , a root of 0 with multiplicity 1 , a root of 1 with multiplicity 1 , and a root of 3 with multiplicity 2 If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?
Answer
A
Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. The curve starts from negative 3 point 8 comma 8, touches the x axis at negative 3 comma 0, passes through the point negative 1 point 5 comma 3 point 5 and comes down to the origin. Here the curve goes down slightly and curves up to the point 2 point 1, curves down to touch x axis at point 2 comma 0 and moves to quadrant I through the point 4 comma 8.
B
Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. It starts from quadrant I passing through the point negative 3 point 8 comma 8 crosses x axis at negative 3 comma 0, goes down and curves up at the point negative 2 comma negative 3 point 5, crosses the y axis at the point 0 comma negative 0 point 8. Here the curve touches the x axis at point 1 comma 0, goes down slightly and again crosses the x axis at point 3 comma 0, and moves to quadrant I through the point 4 comma 7.
C
Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. The curve starts from quadrant III, passing through the point negative 3 point 5 comma negative 8, touches the x axis at 3 comma 0, moves down and curves up at negative 1 point 8 comma 7, and passes through the origin. Here the curve moves up slightly and passes through the point 2 comma 0, goes down, curves up to the point 2 comma negative 2, crosses x axis once again at point 3 comma 0 and moves to quadrant IV through the point 3 point 5 comma negative 8.
D
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. The graph starts from quadrant 3 passing through the point (negative 3 point 5 comma negative 8), it crosses the x axis at (negative 3 comma 0) moves up and curves down at (negative 2 comma 7), crosses the y axis at (0 comma 1), crosses the x axis at (1 comma 0), moves up and curves down at (2 point 5 comma 1). It then moves down, crosses x axis at (2 comma 0) and moves to quadrant 4 through the point (4 comma negative 8).