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Advanced Foundations of Basic Algebra

Algebra

A challenging collection of questions concerning the historical, theoretical, and systematic facts of basic algebra.

mathematics algebra history

10 Questions Hard Ages 16+ Oct 6, 2026

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About this Study Set

This study set covers Algebra through 10 practice questions. A challenging collection of questions concerning the historical, theoretical, and systematic facts of basic algebra. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

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Browse all 10 questions from the Advanced Foundations of Basic Algebra study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 Who is historically credited with introducing the systematic use of the equals sign (=) in 1557 in the book 'The Whetstone of Witte'?

A Robert Recorde
B Leonhard Euler
C René Descartes
D François Viète

2 In the context of the field axioms for real numbers, which property states that a(b + c) = ab + ac?

A Commutative Property
B Associative Property
C Distributive Property
D Reflexive Property

3 What is the formal definition of a 'monic' polynomial?

A A polynomial with only one term
B A polynomial whose highest degree coefficient is 1
C A polynomial with only positive exponents
D A polynomial that cannot be factored

4 Which 9th-century mathematician wrote 'Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala', which provided the etymological origin of the word 'algebra'?

A Diophantus of Alexandria
B Al-Khwarizmi
C Omar Khayyam
D Brahmagupta

5 According to the Fundamental Theorem of Algebra, a non-constant polynomial of degree n with complex coefficients has exactly how many complex roots, counting multiplicity?

A n - 1 roots
B Exactly 1 root
C n roots
D An infinite number of roots

6 What is the correct term for a polynomial expression consisting of exactly two terms?

A Monomial
B Binomial
C Trinomial
D Quadrinomial

7 Which property of equality states that if a = b, then a + c = b + c?

A Transitive Property
B Symmetric Property
C Addition Property of Equality
D Substitution Property

8 In algebra, what is the 'discriminant' of a quadratic equation ax² + bx + c = 0 used to determine?

A The value of x
B The number and type of roots
C The vertex coordinates
D The line of symmetry

9 What is the additive identity element in the set of real numbers?

A 1
B Infinity
C -1
D 0

10 Which mathematician is often referred to as the 'Father of Algebra' for his work 'Arithmetica', which dealt with solving algebraic equations?

A Euclid
B Diophantus
C Pythagoras
D Archimedes

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