# The function f is given by f(x) = mx3+ nx2+ px + q, where m, n, p, q are integers.The graph of f passes through the point (0, 0).(a) Write down the value of q.The graph of f also passes through the point (3, 18).(b) Show that 27m+ 9n + 3p =18.The graph of f also passes through the points (1, 0) and (–1, –10).(c) Write down the other two linear equations in m, n, and p.(d) Find the function in standard form(e) The function f can also be written f (x) = x (x −1)(r x − s) where r and s areintegers. Find r and s.

Question
40 views

The function f is given by f(x) = mx3
+ nx2
+ px + q, where m, n, p, q are integers.
The graph of f passes through the point (0, 0).
(a) Write down the value of q.
The graph of f also passes through the point (3, 18).
(b) Show that 27m+ 9n + 3p =18.
The graph of f also passes through the points (1, 0) and (–1, –10).
(c) Write down the other two linear equations in m, n, and p.
(d) Find the function in standard form
(e) The function f can also be written f (x) = x (x −1)(r x − s) where r and s are
integers. Find r and s.

check_circle

Step 1

(a) the value of q.

Step 2

(b)

Step 3

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in