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 polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, typically expressed as a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

Front

What does it mean to factor by grouping?

Back

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

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

To factor a trinomial of the form ax² + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What are the factors of x² - 9?

Back

The factors of x² - 9 are (x - 3)(x + 3), which is a difference of squares.

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 a common factor?

Back

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

Front

How do you factor 3x² + 12x?

Back

To factor 3x² + 12x, factor out the greatest common factor, which is 3x, resulting in 3x(x + 4).