Polynomials and fractions

2010004403

Level:

Suppose that a trinomial

9 x^{4} + 24 x^{3} y + B^{2}

could be expressed as a square of sum, i.e.

(A + B)^{2}

. Find the product

A

times

B

12 x^{3} y

24 x y

24 x^{2} y

24 x^{3} y

2010004404

Level:

Suppose that a trinomial

25 a^{2} b^{2} + 20 a b^{2} + Y^{2}

could be expressed as a square of sum, i.e.

(X + Y)^{2}

. Find the product

X

times

Y

10 a b^{2}

20 a b^{3}

20 a b^{2}

20 a b

1003032301

Level:

The polynomial

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

equals:

(2 x^{2} + 1) (x^{2} + 3)

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

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

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

1003032302

Level:

The relationship between the time

t

, the travelling distance

s

and the average speed

v

is expressed by the formula

s = v \cdot t

. If the speed doubles, then the time to travel the same distance

will decrease by half.

will decrease by

2

hours.

will double.

will increase by

2

hours.

1003032304

Level:

Reducing the rational expression

\frac{13 a b^{2} (c - d)}{39 a^{2} b (c - d)^{2}}

to lowest terms we get:

\frac{b}{3 a (c - d)}

\frac{3 b}{a (c - d)}

\frac{a}{3 b (c - d)}

3 a b (c - d)

1003032305

Level:

Simplifying the rational expressions

\frac{(x - y)^{2} (p + q)^{3}}{2 (x - y) (p + q)^{4}}

we get:

\frac{x - y}{2 (p + q)}

\frac{p + q}{2 (x - y)}

2 (x - y) (p + q)

2 (x + y) (p - q)

1003032306

Level:

The product

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

equals:

2 x^{3} y + x^{2} y^{2} - 3 x y^{3} - 8 x^{2} y - 12 x y^{2}

2 x^{3} y + 2 x^{2} y^{2} - 3 x y^{3} - 8 x^{2} y - 12 x y^{2}

2 x^{3} y + 3 x^{2} y^{2} - 3 x^{2} y^{2} - 8 x^{2} y - 12 x y^{2}

2 x^{3} y - x^{2} y^{2} + 3 x y^{3} - 8 x^{2} y + 12 x y^{2}

1003032307

Level:

The sum of the polynomials

- x^{3} y^{2} + 6 x y + 5 x y^{4}

and

x^{3} - 4 x y^{4} + y^{2} x^{3} + 2 x y

is:

x^{3} + x y^{4} + 8 x y

- y^{2} + 8 x y + x y^{4} + y^{2} x^{3}

- x^{3} y^{2} + 8 x y + x y^{4} + y^{2} x^{3} + 3 x

x^{3} + x y^{4} + 8 x^{2} y^{2}

1003032308

Level:

Consider polynomials

p (x) = (m - 2) x^{3} + 3 m x^{2} - x + m

and

q (x) = x^{3} + m^{2} x^{2} + x + 3

Polynomials

p

and

q

are different for every

m

Polynomials

p

and

q

are equal for

m = 3

Polynomials

p

and

q

are equal for

m = - 3

Polynomials

p

and

q

are equal for

m = 3

and for

m = 0

2000006101

Level:

Simplify:

3 (3 x^{2} - 5 x + 1) - 2 x^{2} - (4 x^{2} + 2 x - 5)

3 x^{2} - 17 x + 8

3 x^{2} - 13 x + 8

3 x^{2} - 17 x - 2

3 x^{2} - 13 x + 2

Polynomials and fractions

2010004403

2010004404

1003032301

1003032302

1003032304

1003032305

1003032306

1003032307

1003032308

2000006101

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