algebraic expressions are any mathematical formula +, -, x, / ej polynomial functions x2+x=1 a2+b2=1 x/a+y/b=1
A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. An algebraic expression is an expression with a variable in it, and a polynomial is an expression with multiple terms with variables in it.
Algebraic expressions are terms that do not include an equality sign
Basically, an expression is not a polynomial when anything is done that is not allowed in a polynomial - for example, use any variable in the denominator of a monomial, use non-integral powers or radicals (which is basically the same as a non-integral power), use functions, etc.
if it has parentheses
Algebraic expressions are the written relations of or between variables. For example, x2, 1/x, and x + y + z are all algebraic expressions. Algebraic equations are simply algebraic expressions that equate to something. For example, x2 = 4, 1/x = y, and x + y + z = 42 are all algebraic equations. In general, one differentiates algebraic expressions from exponential, trigonometric, hyperbolic, and logarithmic expressions by requiring algebraic expressions to be confined to polynomial expressions. I've added a link regarding polynomials below.
algebraic expressions are any mathematical formula +, -, x, / ej polynomial functions x2+x=1 a2+b2=1 x/a+y/b=1
A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. In another polynomial is a subset of algebraic expression.
An expression is non polynomial if it has : negative exponent fractional exponent variable exponent in the radicand
An algebraic number is one that is a root to a non-zero polynomial, in one variable, whose coefficients are rational numbers.Equivalently, if the polynomial is multiplied by the LCM of the coefficients, the coefficients of the polynomial will all be integers.
A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. An algebraic expression is an expression with a variable in it, and a polynomial is an expression with multiple terms with variables in it.
An algebraic closure is of a field K is an algebraic extension of K which is algebraically closed - that is, it contains a root for every non-constant polynomial in F(x).
no algebraic expressions do not have equal signs but equations do.
Algebraic expressions are terms that do not include an equality sign
A transcendental number is one which is not algebraic. An algebraic number is one which is a root of a non-zero polynomial with rational coefficients.
A polynomial is a type of algebraic expression. They differ in the number of terms that contain variables. An algebraic expression has at least 1 variable, while a polynomial has multiple terms with variables in it.
Basically, an expression is not a polynomial when anything is done that is not allowed in a polynomial - for example, use any variable in the denominator of a monomial, use non-integral powers or radicals (which is basically the same as a non-integral power), use functions, etc.