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 the Greatest Common Factor (GCF)?

Back

The GCF is the largest factor that two or more numbers share. It is used to simplify expressions before factoring.

Front

Factor the polynomial: 3x² + 18x + 15

Back

3(x + 5)(x + 1)

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.

Front

Factor the polynomial: 3x² - 7x + 2

Back

(x - 2)(3x - 1)

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

Factor the expression: 64x³ + 125

Back

(4x + 5)(16x² - 20x + 25)

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree 3, typically in the form ax³ + bx² + cx + d.

Front

Factor the expression: 8x³ - 27

Back

(2x - 3)(4x² + 6x + 9)

Front

What is the sum of cubes?

Back

The sum of cubes is a special factoring pattern that states a³ + b³ = (a + b)(a² - ab + b²).