Polynomials: remainder and factor theorems

Question 1 of 10

The remainder when x² + 3 is divided by (x − 3) is ___

Question 2 of 10

A cubic polynomial has at most

Question 3 of 10

When x³ + px² + qx + 6 is divided by (x − 1) the remainder is 12, and (x + 2) is a factor. Find p and q.

Question 4 of 10

A polynomial of degree 3 can have a degree-4 factor.

Question 5 of 10

Every cubic with real coefficients has at least one real root.

Question 6 of 10

Factorise completely x² − 4x + 3.

Question 7 of 10

Divide x³ + 2x² − 5x − 6 by (x + 1) and state the quotient and remainder.

Question 8 of 10

The remainder when x² + 6 is divided by (x − 5) is ___

Question 9 of 10

The remainder theorem works for division by (x + 3) using f(−3).

Question 10 of 10

Find the remainder when x³ − 2x² − 5x − 2 is divided by (x + 2).