Factoring Test Practice

Front

What is factoring in algebra?

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 factored form of a polynomial?

Back

The factored form of a polynomial is an expression written as a product of its factors, which can be linear or quadratic expressions.

Front

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

Back

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

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax^2 + bx + c.

Front

What is the process to factor a trinomial of the form x^2 + bx + c?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express the trinomial as (x + m)(x + n), where m and n are the two numbers found.

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).

Front

How do you factor a polynomial with a common factor?

Back

To factor a polynomial with a common factor, identify the common factor in all terms, factor it out, and express the polynomial as the product of the common factor and the remaining polynomial.

Front

What is the factored form of 8x^3 - 18x?

Back

The factored form is 2x(2x + 3)(2x - 3).

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to the constant term and add to the coefficient of the linear term, then rewrite the expression as a product of two binomials.

Front

What is the factored form of x^2 + 7x - 30?

Back

The factored form is (x + 10)(x - 3).