Revision/Test (Remainder and Factor Theorem)

1) Given f(x)= x³+ 5x² + 2x -8. Find

A) f(1)

B) f(-2)

C) f(-4)

Hence find all the factors of f(x)

2) Find the values of p and q if (x+3) and (x - 4) are factors of f(x)= x³ - px² - qx +24.

3) Factorise completely:

A) x³ - 7x² - 14x -8.

B) 6x³ - 11x² - 3x + 2.

4) Using factor Theorem, find out whether g(x)= x - 3 is the factor or not of (x)= x³+ x² - 2x - 30.

5) Find the values of p and q if g(x)= x + 2 is a factor of f(x)= x³ - p x² + x + q and f(2)= 4.

6) Find the values of a and b if p(x)= x + 2 is a factor of q(x)= ax³ - b x² + 2(x - 2) and q(2)= 20.

7) Find the remainder when, if g(x)= 2x + 1 is divided f(x)= 2x³ - 3x² - 4x - 5.

8) Find the values of p if the polynomial f(x)= x³ - p x² - x + 3 is divided by g(x)= x² - 1.

9) Find the values of p and q if the polynomial f(x)= px³ + 6x² + qx + 6 is divided by g(x)= x² + 4x + 3.

10) Find the values of q for which the polynomial f(x)= 2x³ + q x² - x - 15 has g(x)= 2x +3 as one of the factors. Hence find the remaining two factors.

11) Find the values of q if the polynomial f(x)= 2x³ + qx² - 7x - 12 is divided by g(x)= x + 4. Hence find all the factors of f(x).

12) Find the values of q if the polynomial f(x)= x³ - 2x² - 13x + q is divided by g(x)= x - 2. Hence find all the factors of f(x).

13) Find the values of p and q, if the polynomial f(x)= px³ + qx² - 8x - 12 is divided by g(x)= x² - 4. Hence find all the factors of f(x).

14) Find the values of p if the polynomial f(x)= x³ + p x² - 16x + 8 is divided by g(x)= x - 2 as one of the factors. Hence find the remaining two factors.