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 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

Factor the expression: x² - 36

Back

(x + 6)(x - 6) - This is an example of the difference of squares.

Front

What is a perfect square trinomial?

Back

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

Front

Factor the expression: x² + 10x + 25

Back

(x + 5)² - This is a perfect square trinomial.

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or expressions.

Front

How do you factor by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.

Front

Factor the expression: 2x² + 8x

Back

2x(x + 4) - The GCF of the terms is 2x.