If p(a)= 0 then (x-a) is a _____ of p(x).

(a)

divisor

(b)

quotient

(c)

remainder

(d)

factor

Zeros of (2-3x) is ______.

(a)

3

(b)

2

(c)

2/3

(d)

3/2

If x - 3 is a factor of p(x), then the remainder is _______.

(a)

3

(b)

-3

(c)

p(3)

(d)

p(-3)

In an expression ax²+bx c the sum and product of the factors respectively____________

(a)

a, bc

(b)

b, ac

(c)

ac, b

(d)

bc, a

Cubic polynomial may have maximum of ________ linear factors.

(a)

1

(b)

2

(c)

3

(d)

4

The remainder when (x²-2x+7) is divided by (x + 4) is __________

(a)

28

(b)

31

(c)

30

(d)

20

The GCD of x⁴-y⁴ and x²-y² is _______.

(a)

x⁴-y⁴

(b)

x²-y²

(c)

(x+y)²

(d)

(x+y)⁴

Show that (x+2) is a factor of x³-4x²-2x+20

If (x -1) divides the polynomial kx³-2x²+25x-26 without remainder, then find the value of k.

Expand (2x+3y)³

Expand the following: (2a-3b+4c)²

Factorise the following: 36m²-49n²

Find: x³-y³, if x-y = 4, xy = 5

Factorise the following: m³+512

Factorise the following: x³+8y³+6xy-1

Is (2x -3) a factor of p(x) = 2x³-9x²+x+12?

If 2x − 3y − 4z = 0 , then find 8x³− 27y³− 64z³

If the quotient obtained on dividing (8x⁴- 2x² + 6x - 7) by (2x +1) is (4x³+ px²- qx + 3), then find p, q and also the remainder.

Factorise x³+13x²+ 32x + 20 into linear factors.

Expand the following:
(i) (x+5)(x+6)(x+4)
(ii) (3x-1)(3x+2)(3x-4)

Verify x³+y³+z³-3xyz = \(\frac{1}{2}\)[x+y+z][(x-y)²+(y-z)²+(z-x)²]

Find the GCD of the following:
(i) (2x + 5), (5x + 2)
(ii) a^m+1, a^m+2, a^m+3
(iii) 2a²+a, 4a²-1
(iv) 3a², 5b³, 7c⁴
(v) x⁴-1, x²-1
(vi) a³- 9ax², (a - 3x)²