Arithmetic with Polynomials and Rational Expressions

IMPORTANT

Mathematics Solutions from Chapter -1 - Arithmetic with Polynomials and Rational Expressions

This chapter consists of topics like Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system etc.

Practice Other Topics from Arithmetic with Polynomials and Rational Expressions

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

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

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x)

This topic covers various concepts like Division of Polynomials, Quotient-Remainder Theorem, etc.

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial

This topic covers various concepts like Factorisation of Expression of Second Degree in two Variables, Factorisation of Homogeneous Expression, etc.

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Prove polynomial identities and use them to describe numerical relationships.

This topic covers various concepts like Algebraic Identity of Cube of Difference, Application of Algebraic Identities, etc.

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined

This topic covers various concepts like Properties Related to nCr, Properties Related to nCr; nCr = nC(n-r), etc.

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system

This topic covers various concepts like Continued Fractions, Operations of Rational Expressions, etc.

Mathematics>Algebra>Arithmetic with Polynomials and Rational Expressions>Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions

This topic covers various concepts like Division of Rational Expressions, Multiplication of Rational Expressions, etc.