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 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 as a sum of terms in descending order of the degree of each term, such as a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c, where a, b, and c are constants.

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 quadratic polynomial?

Back

To factor a quadratic polynomial ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial using these numbers.

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What is the greatest common factor (GCF)?

Back

The greatest common factor is the largest factor that divides two or more numbers or expressions.

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the GCF from each group, and then factor out the common binomial factor.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as a^2 + 2ab + b^2 = (a + b)^2.