FACTORING POLYNOMIALS

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What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler 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 does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means expressing it as a product of its irreducible factors, which cannot be factored further.

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 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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What is the difference of squares?

Back

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

Front

How do you factor a trinomial of the form x² + bx + c?

Back

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 a common factor?

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A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor by grouping?

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

Front

What is the factored form of 4x + 6?

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The factored form of 4x + 6 is 2(2x + 3).