What is factoring in mathematics?

Factoring is the process of breaking down an expression into simpler components, called factors, which when multiplied together yield the original expression. For example, the expression x² - 16 can be factored into (x - 4)(x + 4).

What is the formula for the difference of squares?

The difference of squares states that a² - b² can be factored as (a - b)(a + b). For example, 25 - y² can be factored as (5 - y)(5 + y).

How do you factor a trinomial of the form x² + bx + c?

To factor a trinomial x² + bx + c, find two numbers that multiply to c and add to b. Rewrite the expression as (x + m)(x + n) where m and n are those two numbers. For example, to factor x² + 5x + 6, find 2 and 3, giving (x + 2)(x + 3).

Factor the expression: x² - 10x + 21. Hint: Look for two numbers that multiply to 21 and add to -10.

The numbers -3 and -7 multiply to 21 and add to -10. Thus, x² - 10x + 21 factors to (x - 3)(x - 7).

What is the first step in factoring the expression 4x² - 20x?

The first step is to factor out the greatest common factor (GCF). The GCF of 4x² and -20x is 4x. So, we can factor the expression as 4x(x - 5).

What does it mean to factor an expression?

Factoring an expression means to break it down into simpler components, called factors, that when multiplied together give the original expression. For example, factoring x² - 9 results in (x - 3)(x + 3).

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

Factor the expression: x² + 7x + 10.

Hint: Look for two numbers that multiply to 10 and add to 7.

The numbers 2 and 5 multiply to 10 and add to 7. Therefore, x² + 7x + 10 factors to (x + 2)(x + 5).

What is the first step in factoring the expression 3x² - 12?

The first step is to factor out the greatest common factor (GCF). The GCF of 3x² and -12 is 3. So, we can factor the expression as 3(x² - 4). Next, we can recognize that x² - 4 is a difference of squares, which factors to 3(x - 2)(x + 2).