Factoring Polynomials

Front

What is factoring in mathematics?

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 polynomial?

Back

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

Front

What is the standard form of a quadratic polynomial?

Back

The standard form of a quadratic polynomial is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means expressing it as a product of irreducible factors, which cannot be factored further over the given number system.

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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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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 trinomial of the form x² + bx + c?

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To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n), where m and n are those numbers.

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What is the greatest common factor (GCF)?

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

Front

How do you factor by grouping?

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To factor by grouping, group terms with common factors, factor out the GCF from each group, and then factor out the common binomial factor.

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What is a perfect square trinomial?

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A perfect square trinomial is a trinomial that can be expressed as the square of a binomial, such as a² + 2ab + b² = (a + b)².