### Determine the remainder of the following polynomial divisions using the remainder theorem

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#### Description

A+ TUTORIAL FOR THE FOLLOWING QUESTIONS

Polynomial Functions

Polynomial Inequalities

Polynomial Functions Unit Assignment

1.Determine the remainder of the following polynomial divisions using the remainder theorem:

a.(4x4 + 3x2 - x + 3) (x + 1)

b.(3x2 + 2x - 7) (2x - 1)

(2 marks)

2.Complete the square to find the vertex of each quadratic function. State the vertex.

a.f(x) = x2 + 8x 3

b.f(x) = x2 5x + 8

c.f(x) = 2x2 12x + 1

d.f(x) = 3x2 + 2x 5

(10 marks)

3.Factor each of the following trinomials:

a.y2 + 3y 108

b.15s2 + 26s + 8

c.x4 5x2 36 (hint: let a = x2)

d.t2 + 4t 2

e.2w2 w 4

(14 marks)

4.If (x 3) divides evenly into x3 x2 kx + k, find k.

(2 marks)

5.If (x + 2) is a factor of m2x4 + 5mx3 + x2 7x 2, find m.

(4 marks)

6.When px3 2px2 + 3x p is divided by (x 1), the remainder is -5. Find p.

(2 marks)

7.Let f(x) = ax3 + bx2 + 3x 4. If f(x) is divided by (x 2), the remainder is 2. When it is divided by (x 1), the remainder is -2. Find a and b.

(4 marks)

8.Solve the following polynomial inequalities.

a.4x - 5 ? 2(x - 7

b.x3 - 5x2 + 2x ? -8

c.2(x3 - 2x2 + 3)

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