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 does it mean to factor a quadratic polynomial?

Back

To factor a quadratic polynomial means to express it as a product of two binomials.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as (x + 3) or (2y - 5).

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you factor the expression n² + 16n + 63?

Back

The expression factors to (n + 7)(n + 9).

Front

What is the first step in factoring a quadratic polynomial?

Back

The first step is to identify the coefficients a, b, and c in the standard form ax² + bx + c.

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation; if it is positive, there are two distinct real roots.

Front

How do you factor the expression 5x² - 11x + 6?

Back

The expression factors to (5x - 6)(x - 1).