Factor by Grouping

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What is Factor by Grouping?

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A method used to factor polynomials by grouping terms with common factors.

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What is a polynomial?

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An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

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What does it mean to factor a polynomial?

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To express the polynomial as a product of its factors.

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What is a common factor?

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A number or expression that divides two or more numbers or expressions evenly.

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How do you identify common factors in a polynomial?

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Look for terms that share the same variable and exponent or numerical coefficients.

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What is the first step in factoring by grouping?

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Group the terms of the polynomial into pairs.

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What do you do after grouping terms in factoring by grouping?

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Factor out the common factor from each group.

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What is the significance of the factored form of a polynomial?

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It simplifies the polynomial and makes it easier to solve equations or analyze the function.

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Example of factoring by grouping: Factor 2x^2 + 4x + 3x + 6.

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(2x^2 + 4x) + (3x + 6) = 2x(x + 2) + 3(x + 2) = (2x + 3)(x + 2).

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What is the result of factoring x^2 - 9?

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(x - 3)(x + 3) - This is an example of the difference of squares.