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 the GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that two or more numbers have in common. It is used to simplify expressions before factoring.

Front

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

Back

To factor a quadratic expression, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the expression using these numbers.

Front

What is the factored form of k^2 - 2k - 24?

Back

(k + 4)(k - 6)

Front

What is the factored form of n^2 - 13n + 40?

Back

(n - 5)(n - 8)

Front

What is the factored form of 81m^2 - 1?

Back

(9m - 1)(9m + 1) (This is a difference of squares.)

Front

What is the factored form of 3a^2 + 4a + 1?

Back

(3a + 1)(a + 1)

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 difference between a monomial, binomial, and trinomial?

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in finding roots of the polynomial.