Factoring quadratics

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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 a quadratic expression?

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A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

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What is the general form of a quadratic equation?

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The general form of a quadratic equation is ax² + bx + c = 0.

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What is the purpose of factoring quadratics?

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Factoring quadratics allows us to solve quadratic equations, simplify expressions, and analyze the properties of quadratic functions.

Tags

CCSS.HSA-REI.B.4B

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What is the greatest common factor (GCF)?

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The greatest common factor is the largest factor that divides two or more numbers or expressions.

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How do you factor out the GCF from an expression?

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To factor out the GCF, identify the largest factor common to all terms, divide each term by the GCF, and express the original expression as the product of the GCF and the resulting expression.

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What is the difference of squares?

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The difference of squares is a special factoring pattern that applies to expressions of the form a² - b², which can be factored as (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

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What is the factoring method for a quadratic expression in the form ax² + bx + c?

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To factor a quadratic expression in the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression using these numbers to factor by grouping.

Front

What is the factored form of the expression 12x + 9?

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The factored form is 3(4x + 3).

Tags

CCSS.7.EE.A.1

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What is the factored form of the expression 6x² + 9x?

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The factored form is 3x(2x + 3).