Algebraic Expressions and Polynomials Summary

Algebraic Expressions

• Term: Includes coefficient, variable part (letters/exponents).
• Classifying Polynomials:
  • Monomial: eg. $3x$
  • Binomial: eg. $3x-4$
  • Trinomial: eg. $6x^2+3x-4$
  • Polynomial: eg. $a+b-c+d$ (# terms)
• Degree of a Term: Add the exponents of the variables.
  • Example: $-2x^2y^3z^1 \Rightarrow$ Degree = $2+3+1 = 6$
• Degree of a Polynomial: The highest degree term in the polynomial.

Distribution (Including Adding and Subtracting Polynomials)

• Example: $(3x-2)-(2x-1) = 3x-2-2x+1 = x-1$
• Distribute carefully with negative signs.

Multiplying and Dividing Monomials

• Multiply/divide coefficients and apply exponent rules to variables.
• Example: $(-6x^3y^2)(-x y) = 6x^4y^3$
• Example: $\frac{-24x^5 y^2 z^1}{4x^0 y^2 z^1} = -6x^5$

Simplifying in Algebra

• Remove all brackets before combining like terms.
• Example: $-3x[4-2(x-7)] = -3x[4-2x+14] = -3x[18-2x] = -54x+6x^2$

Area Applications

• Area of a rectangle: $A = lw$
• Example: If $l = 2x$ and $w = 3x^2+1$, then $A = 2x(3x^2+1) = 6x^3+2x$

Finding Missing Factors

• If $36a^3b^5c^2 = (?) (12a^2b^3c)$, then $\frac{36a^3b^5c^2}{12a^2b^3c} = 3ab^2c$