Q4 - HWK 3 - Factoring: GCF, Grouping, & Diff of Sq Review

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What is the definition of the Greatest Common Factor (GCF)?

Back

The GCF of two or more numbers is the largest number that divides all of them without leaving a remainder.

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How do you find the GCF of 3x^2 and 2x?

Back

The GCF is x, as it is the highest common factor of the coefficients (3 and 2) and the variable part (x).

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(q + 11)(q - 11) - This is a difference of squares.

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What is the formula for factoring a difference of squares?

Back

The formula is: a^2 - b^2 = (a + b)(a - b).

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(x + 4)(x - 4) - This is a difference of squares.

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(x + 5)(x - 5) - This is a difference of squares.

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How do you factor using the GCF?

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Identify the largest factor common to all terms, factor it out, and rewrite the expression.

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7(x + 3) - The GCF is 7.

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What is the first step in factoring a polynomial?

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Look for the GCF of all the terms.

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What does it mean if an expression is 'unfactorable'?

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It means that the expression cannot be factored into simpler polynomial expressions.