Factoring Quadratic 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 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 and a ≠ 0.

Front

What does it mean to factor a quadratic polynomial completely?

Back

Factoring a quadratic polynomial completely means expressing it as a product of its linear factors, if possible, and ensuring no further factoring is possible.

Front

What is the GCF (Greatest Common Factor)?

Back

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

Front

How do you factor the expression x² + 5x - 24?

Back

The expression factors to (x + 8)(x - 3).

Front

What is the factored form of 3x² + 18x + 15?

Back

The factored form is 3(x + 5)(x + 1).

Front

How do you factor n² + 7n + 10?

Back

The expression factors to (n + 2)(n + 5).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that applies to expressions of the form a² - b², which factors to (a + b)(a - b).

Front

How do you factor the expression 100x² - 121?

Back

The expression factors to (10x + 11)(10x - 11) using the difference of squares.

Front

What is the factored form of a² - a - 12?

Back

The expression factors to (a - 4)(a + 3).