Factor by grouping practice

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors and then factoring out the common factors.

Front

How do you factor the expression 2n^2 - 8n^3?

Back

Factor out the common term: 2n^2(1 - 4n).

Front

What is the first step in factoring a polynomial?

Back

The first step is to look for a common factor in all the terms of the polynomial.

Front

What does it mean for an expression to be factorable?

Back

An expression is factorable if it can be expressed as a product of two or more factors.

Front

How do you factor the trinomial x^2 - 5x - 36?

Back

Look for two numbers that multiply to -36 and add to -5. The factors are (x + 4)(x - 9).

Front

What is the significance of the zero product property in factoring?

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 the expression 3a^2 + 4a + 3a + 1?

Back

Group the terms: (3a^2 + 4a) + (3a + 1) = a(3a + 4) + 1(3a + 4) = (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.

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

How do you check if your factorization is correct?

Back

You can check by multiplying the factors back together to see if you obtain the original expression.