Algebraic Expressions and Equations

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What is an algebraic expression?

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An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. For example, 3x + 5 is an algebraic expression.

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What is a polynomial?

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A polynomial is an algebraic expression that consists of variables raised to whole number powers and coefficients. For example, 2x^3 - 4x^2 + 3 is a polynomial.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 - x, the degree is 3.

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What are the coefficients in an algebraic expression?

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Coefficients are the numerical factors in terms of an algebraic expression. For example, in 5x^2, 5 is the coefficient.

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What is the zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero. For example, if f(x) = x^2 - 4, the zeros are x = 2 and x = -2.

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How do you multiply two binomials?

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To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

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What is the difference between an expression and an equation?

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An expression is a combination of numbers and variables without an equality sign, while an equation states that two expressions are equal, indicated by an equality sign.

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What is factoring in algebra?

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Factoring is the process of breaking down an expression into simpler components (factors) that, when multiplied together, give the original expression. For example, x^2 - 9 can be factored into (x - 3)(x + 3).

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What is the quadratic formula?

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The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

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What is a linear equation?

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A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.