Factoring Polynomials

Front

Define factoring in algebra.

Back

Factoring in algebra is the process of breaking down an expression into a product of simpler expressions, called factors.

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, such as ax^n + bx^(n-1) + ... + k.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c.

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

Factor the polynomial: x^2 + 5x - 24.

Back

(x + 8)(x - 3)

Front

Factor the polynomial: n^2 + 7n + 10.

Back

(n + 2)(n + 5)

Front

Factor the polynomial: 9x^2 - 25.

Back

(3x - 5)(3x + 5)

Front

Factor the polynomial: 3v^2 - 4v - 7.

Back

(3v - 7)(v + 1)