Factoring Polynomials

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 does GCF stand for in factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers.

Front

How do you find the GCF of 12 and 16?

Back

The GCF of 12 and 16 is 4, as it is the largest number that divides both 12 and 16.

Front

What is the first step in factoring the polynomial 2x^2 + 21x + 10?

Back

The first step is to multiply the coefficient of x^2 (which is 2) by the constant term (which is 10), resulting in 20.

Front

What are the factors of the polynomial 2b^2 + 14b - 16?

Back

The factors are 2(b - 1)(b + 8).

Front

What is the first step in factoring the polynomial 5k^2 - 18k + 9?

Back

The first step is to multiply the coefficient of k^2 (which is 5) by the constant term (which is 9), resulting in 45.

Front

What are the factors of the polynomial 5m^2 - 45m + 90?

Back

The factors are 5(m - 3)(m - 6).

Front

What is the purpose of listing factors when factoring a polynomial?

Back

Listing factors helps to identify pairs of numbers that can be used to rewrite the middle term or to find the roots of the polynomial.

Front

What is the difference between factoring and expanding in algebra?

Back

Factoring is breaking down an expression into simpler components, while expanding is multiplying out the components to form a single expression.