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 consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or expressions without leaving a remainder.

Front

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

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the polynomial using these numbers.

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

What is the sum of cubes formula?

Back

The sum of cubes can be factored using the formula a³ + b³ = (a + b)(a² - ab + b²).

Front

What is the difference of cubes formula?

Back

The difference of cubes can be factored using the formula a³ - b³ = (a - b)(a² + ab + b²).

Front

Factor the polynomial: 3x² - 7x + 2

Back

(x - 2)(3x - 1)

Front

Factor the polynomial: x³ + 2x² - 49x - 98

Back

(x + 7)(x - 7)(x + 2)

Front

Factor the polynomial: x² + 9x - 36

Back

(x + 12)(x - 3)