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 are the roots of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero.

Front

What is the relationship between the factors and roots of a polynomial?

Back

The factors of a polynomial correspond to its roots; if (x - r) is a factor, then r is a root of the polynomial.

Front

How do you factor a quadratic polynomial in the form x² + bx + c?

Back

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

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

What is the sum of cubes formula?

Back

The sum of cubes formula states that a³ + b³ = (a + b)(a² - ab + b²).

Front

What is the product of sums and differences formula?

Back

The product of sums and differences formula states that (a + b)(a - b) = a² - b².

Front

How do you factor a trinomial of the form ax² + bx + c?

Back

To factor ax² + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.