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 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 difference of squares?

Back

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

Front

How do you factor a quadratic polynomial?

Back

To factor a quadratic polynomial, find two numbers that multiply to 'c' (the constant term) and add to 'b' (the coefficient of x).

Front

Factor the polynomial: n² - 13n + 40

Back

(n - 5)(n - 8)

Front

Factor the polynomial: 3v² - 4v - 7

Back

(3v - 7)(v + 1)

Front

What is a perfect square trinomial?

Back

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

Front

Factor the expression: w⁴ - 625

Back

(w² + 25)(w + 5)(w - 5)

Front

What is the sum of cubes formula?

Back

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