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 difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a + b)(a - b).

Front

Factor the expression: x² - 25

Back

(x + 5)(x - 5) - This is an example of the difference of squares.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial, find two numbers that multiply to c and add to b, then express the trinomial as (x + m)(x + n), where m and n are those two numbers.

Front

Factor the expression: v² + 3v - 88

Back

(v + 11)(v - 8) - This is a trinomial that factors into two binomials.

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, including any common factors and irreducible polynomials.

Front

Factor the expression: x² - 17x + 72

Back

(x - 9)(x - 8) - This is a complete factorization of the quadratic.

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.