How do you factor the expression $$6a^2 + 48a - 54$$ ?

First, find the GCF, which is 6. Then factor it out: $$6(a^2 + 8a - 9)$$ . Next, factor the quadratic: $$6(a - 1)(a + 9)$$ .

A binomial is a polynomial with exactly two terms, such as $$x + 5$$ or $$3a^2 - 2b$$ .

A trinomial is a polynomial with exactly three terms, such as $$x^2 + 5x + 6$$ .

How do you factor a trinomial of the form $$x^2 + bx + c$$ ?

Look for two numbers that multiply to $$c$$ and add to $$b$$ . Rewrite the trinomial as a product of two binomials.

What is the difference of squares?

The difference of squares is a special factoring pattern: $$a^2 - b^2 = (a - b)(a + b)$$ .

What is the purpose of factoring in solving equations?

Factoring allows us to rewrite equations in a form that can be easily solved, often by setting each factor to zero.

What is a perfect square trinomial?

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

How do you factor by grouping?

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

What is the role of the leading coefficient in factoring?

The leading coefficient is the coefficient of the highest degree term. It can affect the methods used for factoring, especially in trinomials.

What is the zero product property?

The zero product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ . This is used to solve factored equations.

Factoring Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

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.

2.

FLASHCARD QUESTION

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers share. It is used in factoring to simplify expressions.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is a quadratic expression?

Back

5.

FLASHCARD QUESTION

Front

What does it mean to factor completely?

Back

To factor completely means to break down an expression into its simplest factors, such that no further factoring is possible.

6.

FLASHCARD QUESTION

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get the original expression.

7.

FLASHCARD QUESTION

Front

What is a binomial?

Back

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