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 of the form x² + bx + c?

Back

To factor 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.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

Factor the polynomial: n² - 13n + 40

Back

(n - 5)(n - 8)

Front

Factor the polynomial: k² - 2k - 24

Back

(k + 4)(k - 6)

Front

Factor the polynomial: 3v² - 4v - 7

Back

(3v - 7)(v + 1)

Front

Factor the polynomial: x² - 49

Back

(x + 7)(x - 7)