Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

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 polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, such as ax^n + bx^(n-1) + ... + k.

Front

What does it mean for a polynomial to be factorable?

Back

A polynomial is factorable if it can be expressed as a product of two or more polynomials of lower degree.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

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What is the difference of squares?

Back

The difference of squares is a special factoring pattern expressed as a^2 - b^2 = (a + b)(a - b).

Front

What is the quadratic formula?

Back

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

Front

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

Back

To factor a trinomial, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

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.