Factoring

Front

What is factoring in algebra?

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Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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What is the factored form of a quadratic equation?

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The factored form of a quadratic equation ax^2 + bx + c is (px + q)(rx + s), where p, q, r, and s are constants.

Front

How do you factor a quadratic expression of the form x^2 + bx + c?

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To factor a quadratic expression of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n), where m and n are the two numbers.

Front

What is the difference between factoring by grouping and other factoring methods?

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Factoring by grouping involves rearranging terms in a polynomial to create groups that can be factored separately, while other methods may involve direct application of formulas or patterns.

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What is the first step in factoring by grouping?

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The first step in factoring by grouping is to group the terms of the polynomial into pairs or sets that can be factored individually.

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What is a common factor in factoring?

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A common factor is a number or variable that divides each term of a polynomial, which can be factored out to simplify the expression.

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How do you factor a polynomial with a common factor?

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To factor a polynomial with a common factor, identify the greatest common factor (GCF) of all terms, then divide each term by the GCF and express the polynomial as GCF multiplied by the resulting polynomial.

Front

What is the significance of the zero product property in factoring?

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The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero, which is used to solve equations after factoring.

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What is the factored form of the expression x^2 - 9?

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The factored form of the expression x^2 - 9 is (x - 3)(x + 3), which is an example of the difference of squares.

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What is the process for factoring a cubic polynomial?

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To factor a cubic polynomial, look for a common factor, use synthetic division or long division to factor out a linear term, and then factor the resulting quadratic expression.