Polynomials and fractions

9000101706

Level:

Factor the following polynomial.

8 x^{4} - 48 x^{3} + 72 x^{2}

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

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

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

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

9000101710

Level:

Factor the following polynomial.

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

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

(y - z) {(x - 2 y)}^{2}

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

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

9000146201

Level:

Expand the following expression.

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

8 x^{9} - 12 x^{6} y^{2} + 6 x^{3} y^{4} - y^{6}

8 x^{9} - 4 x^{6} y^{2} + 2 x^{3} y^{4} - y^{6}

8 x^{6} - 12 x^{5} y^{2} + 6 x^{3} y^{4} - y^{5}

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

9000146202

Level:

Expand the following expression.

{(a^{2} + \sqrt{3} b)}^{3}

a^{6} + 3 \sqrt{3} a^{4} b + 9 a^{2} b^{2} + 3 \sqrt{3} b^{3}

a^{6} + \sqrt{3} a^{4} b + 3 a^{2} b^{2} + 3 \sqrt{3} b^{3}

a^{5} + 3 \sqrt{3} a^{4} b + 9 a^{2} b^{2} + 3 \sqrt{3} b^{3}

a^{5} + \sqrt{3} a^{4} b + 3 a^{2} b^{2} + 3 \sqrt{3} b^{3}

9000146207

Level:

Factor the following expression.

4 a^{2} - {(a - 1)}^{2}

(a + 1) (3 a - 1)

(a - 1) (3 a - 1)

(a + 1) (3 a + 1)

(a - 1) (3 a + 1)

9000146208

Level:

Factor the following expression.

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

(x - 4) (3 x + 2)

(x - 4) (3 x - 2)

(x + 4) (3 x + 2)

(x + 4) (3 x - 2)

1003032402

Level:

The polynomial

27 + x^{3}

is equal to a product:

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

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

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

(3 + x)^{3}

1003032403

Level:

Reducing the rational expression

\frac{4 m^{2} - 4 m n + n^{2}}{8 m^{3} - n^{3}}

we get:

\frac{2 m - n}{4 m^{2} + 2 m n + n^{2}}

\frac{m - 4 m n + 1}{2 m - n}

\frac{2 m - n}{4 m^{2} - 4 m n + n^{2}}

\frac{2 m - n}{4 m^{2} + 4 m n + n^{2}}

1003032404

Level:

Simplifying the rational expression

\frac{x^{6} - y^{6}}{x^{2} - y^{2}}

we get:

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

x^{4} - y^{4}

x^{3} - y^{3}

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

1003032502

Level:

Let the polynomial

(x - 2)^{5} - (x + 2)^{5}

be expressed in the form

a_{5} x^{5} + a_{4} x^{4} + a_{3} x^{3} + a_{2} x^{2} + a_{1} x + a_{0}

. Give the sum of

a_{5} + a_{4} + a_{3} + a_{2} + a_{1}

- 180

- 244

- 242

- 212

Polynomials and fractions

9000101706

9000101710

9000146201

9000146202

9000146207

9000146208

1003032402

1003032403

1003032404

1003032502

Events

Akce

Interests

Zajímavosti

About portal

O portálu