Factoring

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 difference of two squares?

Back

The difference of two squares is a special factoring formula that states: a² - b² = (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a quadratic expression in the form ax² + bx + c?

Back

To factor a quadratic expression, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the expression using these numbers to factor by grouping.

Front

What is the greatest common factor (GCF)?

Back

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

Front

How do you find the GCF of two terms?

Back

To find the GCF of two terms, identify the common factors in both terms and multiply them together.

Front

What is the factored form of x² - 25?

Back

The factored form of x² - 25 is (x + 5)(x - 5), which is an example of the difference of two squares.

Tags

CCSS.HSA.APR.C.4

Front

How do you factor the expression 3x² + 5x - 12?

Back

To factor 3x² + 5x - 12, look for two numbers that multiply to -36 (3 * -12) and add to 5. The factors are 9 and -4, leading to the factorization (3x - 4)(x + 3).

Front

What is the factored form of 2x² + 22x + 60?

Back

The factored form of 2x² + 22x + 60 is 2(x + 5)(x + 6).

Front

What is the formula for factoring a perfect square trinomial?

Back

The formula for factoring a perfect square trinomial is a² + 2ab + b² = (a + b)² or a² - 2ab + b² = (a - b)².

Tags

CCSS.HSA.APR.C.4

Front

What is the significance of factoring in solving equations?

Back

Factoring is significant in solving equations because it allows us to rewrite equations in a simpler form, making it easier to find the roots or solutions.

Tags

CCSS.HSA-REI.B.4B