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 does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means expressing it as a product of its irreducible factors, which cannot be factored further over the given number system.

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

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

Back

To factor a quadratic polynomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n), where m and n are the two numbers.

Front

What is the difference of squares formula?

Back

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

Front

How do you factor out the greatest common factor (GCF) from a polynomial?

Back

To factor out the GCF, identify the largest factor common to all terms in the polynomial, then divide each term by the GCF and express the polynomial as GCF multiplied by the resulting polynomial.

Front

What is the factored form of 6x²y - 18xy²?

Back

The factored form is 6xy(x - 3y).

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 is the factored form of x² - 17x + 72?

Back

The factored form is (x - 9)(x - 8).