FACTOR THEOREM
1) Show that x³- 7x²+ 14x -8 is the factor of x -1, then find other factors also.
2) Using factor theorem, find out whether polynomial g(x) is a factor of f(x) or not:
a) Given f(x)= x²+ 3x -10, g(x)= x -2.
b) Given f(x)= 6x² - 5x - 6, g(x)= 2x -3.
c) Given f(x)= 2x² - 5x -12, g(x)= x - 4.
d) Given f(x)= 3x² - 2x -8, g(x)= 3x +4.
e) Given f(x)= 9x²- 4a²+ 4ay - y², g(x)= 3x +2a - y.
f) Given f(x)= x²- 3x²+ 4x -2, g(x)= x -1.
g) Given f(x)= x²(x -14)+ 37x -60, g(x)= x - 2.
h) Given f(x)= x³+ x²- 2x -30, g(x)= x -3.
3) Find the value of k when f(x)= x³ - 3x² - x + k, if g(x)= x +1 is a factor of f(x).
4) Find the values of p and q if g(x)= x +2 is the factor of f(x)= x²- px + x + q and , f(2)= 4.
5) For what value of a is x-2 a factor of f(x)= x² - ax + 6.
6) Find the values of p and q if x+3 and x-4 are factors of x³ - px²- qx + 24.
7) Factorise x³- 7x² + 14x - 8completely.
8) Find the values of p and q if g(x)= x -4 is a factor of f(x)= 4x³- px² + qx -216 and f(-1)= -225.
9) Find the values of a and b if p(x)= x +2 is a factor of q(x)= ax³- bx² + 2(x -2) and q(2)= 20.
10) Find the value of a if x+ a is a factor of f(x)= x³ + a(x² +1) - 2x + 4.
11) Find the remainder, if f(x)= x³- 2x² + x - 3 is divided by g(x)= x +2.
12) Find the remainder, if f(x)= 2x³- 3x² -4x - 5 is divided by g(x)= 2x + 1.
13) If g(x)= 2x -3 is a factor of f(x)= 2x³- 9x² + x + p, find the value of p. Hence find all the factors.
14) If g(x)= 3x - 2 is a factor of f(x)= 3x³ + x² + px + 12, find the value of p. Hence find all the factors of f(x).
15) Find the value of p if the polynomial f(x)= x³- 3x² - px + 24 is divisible by g(x)= x + 3. Hence find all the factors.
16) Find the value of q if the polynomial f(x)= 2x³ + qx² - 7x -12 is divisible by g(x)= x + 4. Hence find all the factors of f(x).
17) Find the value of q if the polynomial f(x)= x³ + 2x² - 13x + q is divisible by g(x)= x -2. Hence find all the factors f(x).
18) Find the value of p if the polynomial f(x)= x³ - px² - x +3 is divisible by g(x)= x² -1. Hence find all the factors.
19) Find the value of p and q if the polynomial f(x)= px³ - 8x -12 + qx² is divisible by g(x)= x² - 4. Hence find all the factors.
Find the value of p and q if the polynomial f(x)= px³ + qx² - 8x -12 is divisible by g(x)= x² - 4. Hence find all the factors.
20) Find the value of p and q if the polynomial f(x)= px³ + 6x² + qx + 6 is divisible by g(x)= x²+ 4x + 3. Hence find all the factors of f(x).
21) Find the value of p for which the polynomial f(x)= x³ + px² - 16x +8 has g(x)= x -2 as one of the factors. Hence find the remaining two factors.
22) Find the value of q for which the polynomial f(x)= 2x³ + qx² - x -15 has g(x)= 2x + 3 as one of the factors. Hence find all the remaining factors.
23) Factorise 6x³ - 11x² - 3x +2. Completely.
