Equivalent expressions of polynomials

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  1. What is a polynomial?
    • Review on Variables, Coefficients, and Expressions
    • What are Monomials, Binomials, and Trinomials?
    • What are the Degree, Leading Term, and Constant term of a polynomial?
    • Name polynomials based on degree: Quadratic, Cubic, Quartic, Quintic, etc.
  2. How to find the degree of a polynomial?
  1. Identify the coefficient and the number of variables for each expression.
    1. 8x8x
    2. 7x2y7{x^2}y
    3. ab - ab
  2. Find the like terms.
    1. 3x3x       7y7y       50x50x       xx       23x223{x^2}
    2. 73a273{a^2}       13a\frac{1}{3}a       3b23{b^2}       0.3c0.3{c^{}}       3a2b3{a^2}b
  3. Combine like terms.
    1. x3+x5+x3x^3 + x^5 + x^3
    2. y2+y5+5y2+x+x2+x{y^2} + {y^5} + 5{y^2} + x + {x^2} + x
    3. z3z3+z2+2x54y3+3z2{z^3} - {z^3} + {z^2} + 2{x^5} - 4{y^3} + 3{z^2}
    4. x2+z2+3x2z24x2x^2 + z^2 + 3x^2 - z^2 - 4x^2
    5. z2+3z+4z334z5{z^2} + 3z + 4{z^3} - {3^4} - {z^5}
    6. 5y2+46y+y23+y5{y^2} + 4 - 6y + {y^2} - 3 + y
  4. 4. Write an equivalent expression with seven terms for each polynomial.
    1. x2+2x+3{x^2} + 2x + 3
    2. y23y3x - {y^2} - 3{y^3} - x
    3. 5x3y+6xy5x - 3y + 6xy
Topic Notes
A polynomial may contain multiple terms. The variable terms have a coefficient and a variable. Terms with the same variables are called like terms, and they can be combined together. It allows us to write equivalent expressions of polynomials with more or less terms.