Question

.POLYNOMIALS
1. The remainder when x³ - px² + 6x – p is divided by x – p is
2. The value of 7³ + 8³ - 15³ is
3. If x -1 is a factor of mx² - √2X + 1 then the value of m is
4. The value of 249² - 248² is
5. Is x + 1 a factor of the polynomial x³ + x² + x + 1
6. Factorise the following
a) x² + 9x + 18 b) 2x² - 7x – 15
c) 2x² -

x +


d) (a – 3b)³ + (3b – c)³ + (c – a)³
e) x³ - 6x² + 3x + 10 f) 2y³ - 5y² - 19y + 42
7. If the polynomials ax³ + 4x² + 3x – 4 and x³ - 4x + a leave the same remainder when divided by
x – 3. Find the value of a
8. If f(x) = x⁴ - 2x³ + 3x² - ax + b is a polynomial such that when it is divided by x -1 and x + 1 the
reminders are respectively 5 and 19. Determine the remainder when f(x) is divided by x -2.
9. If ax³ + bx² + x – 6 has x + 2 as a factor and leaves a remainder 4 when divided by x -2, find the
values of a and b.
10. Find the value of a and b so that x + 1 and x – 1 are factors of x⁴ + ax³ - 3x² + 2x + b
11. If x³ + ax² - bx + 10 is divisible by x² - 3x + 2, find the values of a and b
12. If both x – 2 and x -

are factors of px² + 5x + r show that p = r
13. Factorise p³(q – r)³ + q³(r – p)³ + r³(p – q)³
14. Factorise 9(x – 2y)² - 4(x – 2y) – 13.
15. If a + b = 8 and ab = 6, find the value of a³ + b³

Answer 1

1):-

remainder=p³-p(p)²+6(p)-p,

remainder=p³-p³+6p-p,

=5p,


2):-

7³+8³-15³,

3×7×8×-15,

-2520,


3):-

m(1)²-√2×1+1=0,

m-√2+1=0,

then

m=√2-1,


4):-

249²-248²,

(249+248) (249-249),

497×1,

497,


5):-


(-1)³+(-1)²+(-1)+1,

-1+1-1+1,

0, yes x+1 is a factor,


6):-


a):-
(x+6)(x+3),

b):-
(2x+3)(x-5),


c):- check your question i think something missing in this question,

d):-
3×(a-3b)×(3b-c)×(c-a),


i think it is enough for 5 points....