Polynomials and fractions

1003032503

Level:

The polynomial

3 x^{5} + p x^{3} - (p - 1) x^{2} + 5 x - 9

is divisible by the binomial

x^{2} - 1

p

is equal to:

- 8

- 16

4

6

1003032505

Level:

Factoring the polynomial

x^{4} + 4

you get:

(x^{2} - 2 x + 2) (x^{2} + 2 x + 2)

(x^{2} + 2) (x^{2} - (- 2))

{(x + \sqrt{2})}^{4}

(x^{2} - \sqrt{2} x + 2) (x^{2} + \sqrt{2} x + 2)

1003032506

Level:

In a parallel circuit the total resistance

R

of three components with the resistances

R_{1}

R_{2}

R_{3}

is given by the formula

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

. Express

R_{1}

from this formula.

R_{1} = \frac{R R_{2} R_{3}}{R_{2} R_{3} - R (R_{2} + R_{3})}

R_{1} = \frac{R - R_{2} - R_{3}}{R R_{2} R_{3}}

R_{1} = R - \frac{R_{2} R_{3}}{R_{2} + R_{3}}

R_{1} = \frac{R_{2} R_{3} - R (R_{2} + R_{3})}{R R_{2} R_{3}}

1003032507

Level:

Express

v_{1}

from the formula

v = \frac{v_{1} v_{2} (d_{1} + d_{2})}{d_{1} v_{2} + d_{2} v_{1}}

v_{1} = \frac{v d_{1} v_{2}}{v_{2} d_{1} + v_{2} d_{2} - v d_{2}}

v_{1} = \frac{v v_{2} d_{1}}{v d_{2} - v_{2} d_{1} - v_{2} d_{2}}

v_{1} = \frac{v v_{2} (d_{1} + d_{2})}{d_{1} v_{2} + d_{2} v}

v_{1} = \frac{v (d_{1} v_{2} + d_{2} v_{1})}{v_{2} (d_{1} + d_{2})}

1003032508

Level:

Find the term that does not contain

x

and

y

(constant term) in the expansion of

(x + y)^{4} (\frac{1}{x} + \frac{1}{y})^{4}

70

2

36

0

2000002609

Level:

The equation

x^{3} + 27 = 0

can be solved by factoring. The expression on the left can be factored as:

(x + 3) (x^{2} - 3 x + 9)

(x + 3) (x^{2} + 3 x + 9)

(x + 3)^{3}

(x - 3) (x^{2} + 3 x + 9)

2010000802

Level:

The polynomial

2 x^{5} - p x^{3} + (p - 1) x^{2} + 2 x - 5

is divisible by the binomial

x^{2} + 1

p

is equal to:

- 4

- 8

4

8

2010000803

Level:

Factoring the polynomial

- 4 x^{4} + 24 x^{3} - 36 x^{2}

you get:

- 4 x^{2} (x - 3) (x - 3)

- 4 x^{2} (x + 3) (x + 3)

- 4 x^{2} (x + 3) (x - 3)

- 4 x^{2} (x^{2} + 6 x - 9)

2010000804

Level:

Factoring the polynomial

- 3 x^{5} - 24 x^{4} - 48 x^{3}

you get:

- 3 x^{3} (x + 4) (x + 4)

- 3 x^{3} (x - 4) (x - 4)

3 x^{3} (4 - x) (4 - x)

3 x^{3} (x + 4) (x - 4)

2010000805

Level:

In a parallel circuit the total resistance

R

of three components with the resistances

R_{1}

R_{2}

R_{3}

is given by the formula

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

. Express

R_{2}

from this formula.

R_{2} = \frac{R R_{1} R_{3}}{R_{1} R_{3} - R (R_{1} + R_{3})}

R_{2} = \frac{R - R_{1} - R_{3}}{R R_{1} R_{3}}

R_{2} = R - \frac{R_{1} R_{3}}{R_{1} + R_{3}}

R_{2} = \frac{R_{1} R_{3} - R (R_{1} + R_{3})}{R R_{1} R_{3}}

Polynomials and fractions

1003032503

1003032505

1003032506

1003032507

1003032508

2000002609

2010000802

2010000803

2010000804

2010000805

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