Factoring trinomials

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.

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What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax^2 + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

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

Back

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

Front

What is the Greatest Common Factor (GCF)?

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The GCF is the largest factor that divides two or more numbers or terms without leaving a remainder.

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.

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What is the difference between factoring and expanding an expression?

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Factoring is breaking down an expression into its factors, while expanding is multiplying out the factors to obtain the original expression.

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What are the roots of a quadratic equation?

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The roots of a quadratic equation are the values of x that make the equation equal to zero, found using factoring, completing the square, or the quadratic formula.

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What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

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How do you factor a difference of squares?

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A difference of squares can be factored using the formula a² - b² = (a + b)(a - b).