General Knowledge Quiz

Study Notes

Capitals of Countries

Paris is the capital of France

Noble Gases

Helium, neon, argon, krypton, xenon, and radon are noble gases.

Human Anatomy

The human body has two lungs, not four.

Planets and Characteristics

Hardness of Materials

Diamond is the hardest natural substance on Earth.

Polynomials

Polynomials are expressions made up of variables, constants, and exponents.
They are combined using addition, subtraction, multiplication and division, but not division by a variable.
Polynomials are classified based on the number of terms present:
- Monomial: One term
- Binomial: Two terms
- Trinomial: Three terms
- Multinomial: Four or more terms

Types of Polynomials

Literal Coefficient: The symbol or letter in a particular expression.
Numerical Coefficient: The numeral/number in a particular expression.
Degree of a Term: The sum of the exponents of its variables.
Degree of a Polynomial: The highest exponent found in any non-zero term of the polynomial.

Operations on Polynomials

Addition of Monomials:
- Add similar terms by finding the sum of their numerical coefficients and prefixing it to their common literal factor.
- Use the addition laws of signed numbers:
  - For numbers with the same sign, find their sum and bring down the common sign.
  - For numbers with different signs, find their difference and bring down the sign of the number with the greater numerical value.
- Dissimilar terms cannot be directly added and can only be indicated as a sum.
Addition of Polynomials:
- Can be done in two ways: horizontal form and vertical form.
- In horizontal form, simply combine similar terms.
- In vertical form, align the terms with the same variable and exponent and add their coefficients.
Subtraction of Monomials:
- Similar terms: Change the sign of the subtrahend and proceed with algebraic addition.
- Dissimilar terms: The subtraction can only be indicated. Change the sign of the subtrahend.
Subtraction of Polynomials:
- Change the sign of each term in the second polynomial and proceed with addition.
Multiplication of Monomials:
- Find the product of numerical coefficients.
- Add exponents of the same variable.
- Apply index laws.
Multiplication of a Polynomial by a Monomial:
- Multiply each term in the polynomial by the monomial, using the distributive law of multiplication.
- Arrange the answer in ascending or descending powers of one of the letters.
Multiplication of Polynomials:
- Use the distributive law of multiplication or the long method.
- Arrange the expressions in descending or ascending order before multiplying.