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

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

IMPORTANT

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: Overview

This topic covers various concepts like Multiplication of Polynomials, Subtraction of Polynomials, etc.

Important Questions on 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

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Mathematics>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> Q 1

When polynomial $f (x) = x^{4} + 2 x^{3} - 3 x^{2} + x - 1$ is divided by $(x - 2)$ , then what will be remainder?

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Mathematics>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> Q 2

Obtain all the zeros of polynomial $x^{3} - 7 x + 6$ , if one of its zeros is $1$ .

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Mathematics>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> Q 3

If $2$ and $- 2$ are two zeros of the polynomial $2 x^{4} - 5 x^{3} - 11 x^{2} + 20 x + 12$ , find all the zeros of the given polynomial.

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Mathematics>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> Q 4

Divide $4 x^{3} - x + 1$ by $2 x - 1$ .

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Mathematics>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> Q 5

Radha taught her sister Sonia to find the factors and multiples of numbers and even polynomials, using division algorithm. After the detailed lecture, Radha asked Sonia to find a factor of the polynomial $\frac{42 x^{3} - 15 x^{2} - 84 x + 18}{- 7 x^{2} - 8 x + 2}$ . What could be the possible factor Sonia may have found?

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Mathematics>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> Q 6

On dividing $x^{3} - 3 x^{2} + 5 x - 7$ by $x^{2} - 2 x + 4$ , if the remainder is in the form of $A x + B$ then find the values of $A and B$ .

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Mathematics>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> Q 7

How are we supposed to divide a polynomial by a monomial?

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Mathematics>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> Q 8

Obtain other zeroes of the polynomial $f (x) = 2 x^{4} + 3 x^{3} - 5 x^{2} - 9 x - 3$ , if two of its zeroes are $\sqrt{3}$ and $- \sqrt{3}$ .

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Mathematics>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> Q 9

What is the quotient and remainder of $(2 x^{3} - 8 x^{2} + 16 x - 30) \div (2 x^{2} + x - 1)$ .

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Mathematics>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> Q 10

What is the quotient and remainder of $(4 x^{3} + 5 x^{2} - 2 x + 8) \div (2 x + 1)$ .

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Mathematics>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> Q 11

Find roots of the cubic polynomial $x^{3} + 8 x^{2} + 17 x + 10 = 0$ .

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Mathematics>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> Q 12

If $x^{3} - 3 x^{2} + 3 x + 7 = (x + 1) (a x^{2} + b x + c)$ , then find the value of $a + b + c$ .

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Mathematics>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> Q 13

Government of Delhi allotted Relief Fund to help the families whose houses and shops were burned in a fire accident.

The fund is represented by $6 x^{3} - 11 x^{2} + 15 x - 24$ .

The fund is equally divided between each of the families of that accident. Each family receives an amount of $₹ 3 x - 7$ . After distribution, $₹ 7 x + 11$ amount is left. The District Magistrate decide to use this amount to develop the infrastructure of the area. Find the number of families which received relief fund from Government.

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Mathematics>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> Q 14

A polynomial $f (x)$ with rational coefficients leaves remainder $15$ , when divided by $x - 3$ and remainder $2 x + 1$ , when divided by ${(x - 1)}^{2}$ . Find the remainder when $f (x)$ is divided by $(x - 3) {(x - 1)}^{2}$ .

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Mathematics>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> Q 15

Divide the polynomial $P (x) = x^{3} - 3 x^{2} + 5 x - 3$ by the polynomial $g (x) = x^{2} - 2$ and find quotient and remainder.

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Mathematics>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> Q 16

What is the quotient and remainder when $12 x^{3} - 8 x^{2} - 6 x + 10$ is divided by the polynomial $(3 x - 2)$

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Mathematics>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> Q 17

${(x^{2} + 2 x + 1)}^{2} \div x^{2}$

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Mathematics>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> Q 18

The value of $a$ and $b$ for which $x^{4} + x^{3} + 8 x^{2} + a x + b$ is divisible by $x^{2} + 1$ is:

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Mathematics>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> Q 19

Divide the following

$p (x) = x^{4} - 3 x^{2} + 4 x + 5 g (x) = x^{2} - x + 1$

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Mathematics>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> Q 20

Find the polynomial of least degree which should be subtracted from the polynomial $x^{4} + 2 x^{3} - 4 x^{2} + 6 x - 3$ so that it is exactly divisible by $x^{2} - x + 1$ .