Factoring Polynomials and Expressions

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler 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 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 a perfect square trinomial?

Back

A perfect square trinomial can be factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

Front

Factor the expression: d² - 10d + 25

Back

(d - 5)(d - 5) or (d - 5)².

Front

What is the method to factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to the constant term (c) and add to the linear coefficient (b).

Front

Factor the expression: k² + 7k + 10

Back

(k + 2)(k + 5).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring case where a² - b² = (a + b)(a - b).

Front

Factor the expression: x² + 7x - 30

Back

(x + 10)(x - 3).