If4is a zero of the cubic polynomialx33x210x24 find its other two zeroes

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

If

\sqrt{3}

and

- \sqrt{3}

are the zeroes of the polynomial

2 x^{4} - 3 x^{3} - 5 x^{2} + 9 x - 3

. Find the other two zeroes of the polynomial.

HARD

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

The remainder when the polynomial

1 + x^{2} + x^{4} + x^{6} + . . . . . + x^{22}

is divided by

1 + x + x^{2} + x^{3} + . . . . . + x^{11}

is

EASY

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

By using division algorithm method find quotient and remainder when polynomial $P (x) = x^{4} - 3 x^{2} + 4 x - 3 is divided by g (x) = x^{2} + 1 - x$

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Find the other two zeroes of the polynomial

3 x^{4} - 23 x^{3} + 62 x^{2} - 68 x + 24

, if two of its zeroes are

2

and

3

.

EASY

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

4 x^{3} + 12 x^{2} - x - 3

is divisible by

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Obtain all other zeroes of $3 x^{4} + 6 x^{3} - 2 x^{2} - 10 x - 5$ , if two of its zeroes are $\sqrt{\frac{5}{3}}$ and $- \sqrt{\frac{5}{3}}$ .

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Divide the polynomial $p (x)$ by the polynomial $g (x)$ , and find the quotient and the remainder.

$p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}$

HARD

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

All the zeroes of the polynomial

x^{3} + 2 x^{2} + a

are also zeroes of the polynomial

x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x + b

. Then, the values of

a

and

b

are respectively:

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

C_{0} C_{r} + C_{1} C_{r + 1} + C_{2} C_{r + 2} + \dots + C_{n - r} C_{n}

is equal to

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Find all zeroes of the polynomial $(2 x^{4} - 9 x^{3} + 5 x^{2} + 3 x - 1)$ if two of its zeroes are $(2 + \sqrt{3})$ and $(2 - \sqrt{3})$ .

HARD

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

The equation

166 \times 56 = 8590

is valid in some base

b \geq 10

(that is,

1, 6, 5, 8, 9, 0

are digits in base

b

in the above equation). Find the sum of all possible values of

b \geq 10

satisfying the equation.

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Polynomial

x^{4} + x^{3} - 2 x^{2} + x + 1

is divided by

x - 1

, the remainder will be

HARD

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Find the number of ordered triples

(x, y, z)

of real numbers that satisfy the system of equation

x + y + z = 7; x^{2} + y^{2} + z^{2} = 27; x y z = 5

EASY

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Divide

2 x^{2} + 3 x + 1

by

x + 2

.

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

If

(a x + b) (x^{5} + 1) - (5 x + 1)

is divisible by

x^{2} + 1

, then the value of

2 a + 3 b

is

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

If

3 x^{2} - x^{3} + 5 x - 2

is divided by

x - 1 + x^{2}

, then the remainder is

EASY

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

When

2 x^{2} + 3 x + 1

is divided by

x + 2

then quotient and remainder are:

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

Divide the polynomial $f (x) = 3 x^{2} - x^{3} - 3 x + 5$ by the polynomial $g (x) x - 1 - x^{2}$ and verify the division algorithm

MEDIUM

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

{(x + 1)}^{4}

is divided by

(x - 1)^{3}

. Then, the value of the remainder at

x = 1

is

HARD

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials

For real numbers

p, q

and

a

, if the polynomial

x^{3} - 3 p x + 2 q

is divisible by the polynomial

x^{2} + 2 a x + a^{2}

, then which
of the following is correct?

If $4$ is a zero of the cubic polynomial $x^{3} - 3 x^{2} - 10 x + 24$ , find its other two zeroes.

Important Questions on Arithmetic with Polynomials and Rational Expressions

Learn and Prepare for any exam you want !

If 4 is a zero of the cubic polynomial x3-3x2-10x+24, find its other two zeroes.

Important Questions on Arithmetic with Polynomials and Rational Expressions

Learn and Prepare for any exam you want !

If $4$ is a zero of the cubic polynomial $x^{3} - 3 x^{2} - 10 x + 24$ , find its other two zeroes.