Factoring Polynomial

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into simpler components, called factors, that when multiplied together give the original expression.

Front

What does GCF stand for?

Back

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

Front

How do you factor out the GCF from an expression?

Back

To factor out the GCF, identify the largest factor common to all terms in the expression and divide each term by this factor, then write the expression as the product of the GCF and the remaining terms.

Front

What is a trinomial?

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial that consists of two terms, usually in the form a + b or a - b.

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 trinomial like x^2 - 6x + 9?

Back

To factor x^2 - 6x + 9, look for two numbers that multiply to 9 and add to -6. The factors are (x - 3)(x - 3) or (x - 3)^2.

Front

What is the factored form of x^2 - 144?

Back

The factored form of x^2 - 144 is (x + 12)(x - 12), using the difference of squares.

Front

What is the factored form of 9x^2 - 25?

Back

The factored form of 9x^2 - 25 is (3x - 5)(3x + 5), also using the difference of squares.

Front

How do you factor a trinomial completely?

Back

To factor a trinomial completely, first look for a GCF, then factor the remaining trinomial into two binomials.