Factoring Quadratics

Front

What does GCF stand for in factoring quadratics?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in a polynomial.

Front

How do you find the GCF of a polynomial?

Back

To find the GCF of a polynomial, identify the common factors of each term and select the highest power of each common factor.

Front

What is the first step in factoring a trinomial?

Back

The first step in factoring a trinomial is to identify the coefficients of the quadratic equation in the form ax^2 + bx + c.

Front

What is the factored form of a trinomial?

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The factored form of a trinomial is expressed as (x + p)(x + q), where p and q are the roots of the equation.

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How do you factor the expression 24c^5 - 12c^3?

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To factor 24c^5 - 12c^3, first find the GCF, which is 12c^3, and then factor it out: 12c^3(2c^2 - 1).

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What are the steps to factor a quadratic expression?

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1. Identify the coefficients a, b, and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the expression using these numbers. 4. Factor by grouping.

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What is the significance of the roots in factoring quadratics?

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The roots of a quadratic equation are the values of x that make the equation equal to zero, and they are used to express the quadratic in its factored form.

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How do you factor x^2 + 11x + 24?

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To factor x^2 + 11x + 24, find two numbers that multiply to 24 and add to 11, which are 8 and 3. Thus, it factors to (x + 8)(x + 3).

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What is the factored form of x^2 + 7x + 12?

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The factored form of x^2 + 7x + 12 is (x + 3)(x + 4).

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What is the process of factoring out a common term?

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Factoring out a common term involves identifying the highest common factor in all terms of the expression and rewriting the expression as the product of that factor and the remaining terms.