Factoring quadratics

Front

What is factoring in algebra?

Back

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.

Front

What is a quadratic expression?

Back

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

Front

What is the general form of a quadratic equation?

Back

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

Front

What are the factors of the expression x² - 81?

Back

The factors of x² - 81 are (x - 9)(x + 9), which is a difference of squares.

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How do you factor out the greatest common factor (GCF)?

Back

To factor out the GCF, identify the largest factor that divides all terms in the expression, then divide each term by the GCF and write it outside the parentheses.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a² - b² = (a - b)(a + b).

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How do you factor the expression 5x³ - 7x²?

Back

To factor 5x³ - 7x², first factor out the common term x², resulting in x²(5x - 7).

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What is the factored form of 6m² + 16m?

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The factored form of 6m² + 16m is 2m(3m + 8), where 2m is the GCF.

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What is the purpose of factoring quadratics?

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

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.