Polynomials: remainder and factor theorems

Question 1 of 10

Find the sum of the roots of x³ − 7x² + 14x − 8 = 0.

Question 2 of 10

The remainder theorem states that when f(x) is divided by (x − a) the remainder is

Question 3 of 10

Show that (x − 2) is a factor of f(x) = x³ − 3x² − 4x + 12 and factorise f(x) completely.

Question 4 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 5 of 10

Find the remainder when x³ − 2x + 3 is divided by (x − 3).

Question 6 of 10

Factorise completely x² − 8x + 16.

Question 7 of 10

The remainder when x² − 1 is divided by (x − 1) is 1.

Question 8 of 10

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

Question 9 of 10

The degree of the polynomial 3x⁴ − 2x + 1 is

Question 10 of 10

Factorise completely x² − 2x + 1.