Mastering Math: Exponents, Roots, Polynomials, and More

Posted on Jan 29, 2025 in Statistics

Powers

Power = (Base)exponent

Properties of Powers

  • 1st
  • 2nd
  • 3rd
  • 4th
  • 5th
  • 6th
  • 7th
  • 8th
  • 9th

Scientific Notation

A) Mt indicates the number of zeros to the right.

B) Mor indicates tenths. No. If I have a high ten, and M is positive, add zeros to the number as indicated by the M.

Roots

A) Numeric values of a radical. If the radical is a positive number, the solution is a unique positive root.

B) If the radical is negative and the index is even, the solution is a negative root.

C) Based on a positive, even index, there is a double negative and positive solution.

D) Based on a negative, even index, there is no solution in the real numbers.

To put power in superscript, it is marketed as the radical base. With an exponent as a fraction, the numerator is the radicand exponent, and the denominator is the index.

Operations of a Radical

  • Factoring the radical.
  • Divide the exponent of each factor by filing (where equal or greater than the index) by the index.

The splitting ratio is the number of factors that go out, the rest by filing, and those that are within.

Products and Division

  • Make the least common multiple (LCM) of the indices.
  • Divide the LCM for each index and raise the result that corresponds to each radicand.
  • The index of the result is the LCM.
  • Multiply the coefficient.

Streamline

1. The denominator is a square root. Multiply the numerator and denominator by the coefficient.

2. The denominator is greater than index root 2. Multiply the numerator and denominator by the root of the denominator raised to an exponent, which is the difference between the rate of radical and radicand exponent of the root of the denominator.

3. When the denominator is a binomial, multiply the denominator and the numerator by the conjugate of the denominator.

2-x Opposed Conjugated = -2 + x 2 + x

(a + b) (a – b) = (a)2 – (b)2 = Variance Sum of squared difference

Sum Squared (Binomial)

(a + b)2 = (a)2 + (b)2 + 2(a)(b) (-ab)2

Difference Squared

(a + b)2 = (a)2 + (b)2 – 2(a)(b)

(-a + b)2

Polynomials

Numerical value: The unknown is replaced by the value that it tells me.

Addition and Subtraction

Only you can add or subtract like monomials (same letters with equal exponents), which is added or subtracted are the coefficients.

Products

Multiply each term of the first polynomial by each term of the second polynomial (signs with signs, numbers with numbers, and letters with letters in the same base by adding the exponents).

Division

  1. Complete and order the dividend and the divisor from the highest to the lowest degree.
  2. Divide the first term of the dividend from the first term of the divisor.
  3. Multiply the quotient by dividing each term of the changing sign and place the column you extent appropriate for the dividend. Add and subtract from the operation of paragraph 2.

Factoring

  1. Scared common factor (the number that divides all terms or words that all the terms and the highest grade) who take record common factor is to divide each term by a common factor.
  2. Use the remarkable identities.
  3. Apply Ruffini’s rule. Ended dividers are valid independent. Only those who give me “=” in the rest of the division. If the rest gave me “0”, for instance, by making four factor Ruffini will x-4, however, if I gave to -3, the factor will be x+3.

The factors will be those taking the obtained common factor which alle Ruffini using or identities and the last significant coefficient of the division. Only I will enforce the remainder 0.

Biquadratic

Be decided by a quadratic equation, but there is the x2

x2 =

Higher than 3

It is factored, and each factor is equal to 0.