Question

What is the end behaviors of polynomial B(x) = (x-5)^2 (x+2)^2 (x)^2 (x-3) ?

Also if you anyone can please graph that thank thank you!!!

Answer 1

• for x approaching -∞, B(x) approaches -∞
• for x approaching +∞, B(x) approaches +∞

Explanation:

The polynomial has odd degree (7) and a positive leading coefficient (1), so has a general shape that is rising from left to right (/). That is, the sign of the end value of B(x) matches the sign of x.

The double zeros at -2, 0, +5, and the single zero at 3 mean the graph will touch the x-axis, but not cross, at x=-2 and 0; it will cross at x=3; and it will touch, but not cross at x=5. The graph is attached.