Polynomials-Test

( 2.0 marks)

The polynomials P(t) = 4t³ - st² + 7 and Q(t) = t² + st + 8 leave the same remainder when divided by (t - 1). Find the value of s.

( 2.0 marks)

Find the value of k for which the cubic polynomial is exactly divisible by

( 2.0 marks)

Verify whether the indicated numbers are zeroes of their corresponding polynomials.

(a)   Q(s) = -4s³ + 7s² - 24; s = -4 and 1

1 marks

(b)   

1 marks

( 2.0 marks)

If x = -2 is a root of the polynomial P(x) = -2x⁴ - 7x³ - 3x² - tx - 10, then find the value of t.

( 3.0 marks)

State whether the following statements are true or false. Give reasons to justify your answers.

(a)   The degree of polynomial -5x⁵ - 6x⁴ - 8x² is 4.

1 marks

(b)   The algebraic expression is a polynomial.

1 marks

(c)   The polynomial is a quadratic trinomial.

1 marks

( 3.0 marks)

Using the long division method, determine the remainder when the polynomial 4x⁵ + 2x⁴ - x³ + 4x² - 7 is divided by (x - 1).

( 3.0 marks)

Evaluate the following products using algebraic identities.

(a)   993³

(b)   1002³

(4.0 marks)

If then find the value of

(3.0 marks)

Using a suitable identity, determine the value of A) (17)³ + (-12)³ + (-5)³ and B) 64m³- 343n³

(6.0 marks)

Factorise:

A)   2y³ - 4y² - 2y + 4

B)   2x² + 7x + 3

C)   x³ + 13x² + 32x + 20