Factoring Polynomials

Front

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 is a cubic polynomial?

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A cubic polynomial is a polynomial of degree three, which means its highest exponent is three. It can be expressed in the form ax³ + bx² + cx + d.

Front

What does it mean to factor completely?

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To factor completely means to break down a polynomial into its simplest factors, such that no further factoring is possible.

Front

What is the difference between a monomial, binomial, and trinomial?

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A monomial has one term, a binomial has two terms, and a trinomial has three terms.

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What is the first step in factoring by grouping?

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The first step in factoring by grouping is to group the terms of the polynomial into pairs or sets that can be factored separately.

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What is the difference of squares?

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The difference of squares is a special factoring pattern that applies to expressions of the form a² - b², which can be factored as (a + b)(a - b).

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How do you factor a polynomial with four terms?

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To factor a polynomial with four terms, you can use the method of grouping, where you group the terms into two pairs and factor out the common factors.

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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

What is the role of the leading coefficient in a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial, and it determines the polynomial's end behavior.