Factoring Polynomials including Grouping and Cubic Equations

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

Front

What does it mean to factor a quadratic polynomial?

Back

Factoring a quadratic polynomial involves expressing it in the form (ax + b)(cx + d), where the product equals the original polynomial.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a trinomial of the form ax^2 + bx + c?

Back

To factor a trinomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the grouping method in factoring?

Back

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

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree three, typically expressed in the form ax^3 + bx^2 + cx + d.

Front

How do you factor a cubic polynomial?

Back

To factor a cubic polynomial, look for a common factor, use synthetic division, or apply the Rational Root Theorem to find possible roots.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution of a polynomial equation is a factor of the constant term divided by a factor of the leading coefficient.

Tags

CCSS.HSA.APR.B.2