Factor

A chalkboard illustrating the algebraic process of factoring the difference of squares, showing x² - 9 factored into (x - 3)(x + 3).
The image exhibits the factoring technique used in algebra to break down expressions into simpler multipliers, highlighting the classic difference of squares formula.

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Factors in Math

A factor of an expression is a quantity that divides the expression without leaving a remainder. Factoring refers to expressing a mathematical expression as a product of its factors. Factors are always positive whole numbers.

Factoring is an essential skill in algebra, often used to simplify expressions, solve equations, and understand the structure of mathematical relationships.

Examples of Factoring

  1. Factoring a Constant:  6=2\times3, Here, 2 and 3 are factors of 6. Factoring 6  involves expressing it as a product of its prime factors.

  2. Factoring a Linear Expression: x+5, This expression can be factored by taking out the common factor, which is 1 in this case. x+5=1\times(x+5)

  3. Factoring a Quadratic Expression: x^2-4x+4, This quadratic expression can be factored as (x-2)(x-2)\text{ or }(x-2)^2.

  4. Factoring by Grouping: xy+3x+2y+6, Grouping the terms allows for factoring by common factors: (xy+3x)+(2y+6)=x(y+3)+2(y+3)=(x+2)(y+3)

  5. Factoring a Difference of Squares: a^2-b^2, This expression can be factored as (a-b)(a+b).

  6. Factoring a Trinomial: x^2+5x+6, This trinomial can be factored as (x+2)(x+3).

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Cross-Multiplication

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Polynomial

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The Art of Factoring

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