Factor the expression 4x^2 - 16.

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What’s inside this PDF?

Question: Factor the expression 4x^2 - 16.

Options:

4(x - 4)(x + 4)
4(x^2 - 4)
(2x - 4)(2x + 4)
4(x - 2)(x + 2)

Correct Answer: 4(x - 4)(x + 4)

Solution:

First, factor out the greatest common factor, which is 4. This gives us 4(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 4(x - 2)(x + 2).

Factor the expression 4x^2 - 16.

Practice Questions

Factor the expression 4x^2 - 16.

4(x - 4)(x + 4)
4(x^2 - 4)
(2x - 4)(2x + 4)
4(x - 2)(x + 2)

Questions & Step-by-Step Solutions

Factor the expression 4x^2 - 16.

Step 1: Look at the expression 4x^2 - 16.
Step 2: Identify the greatest common factor (GCF) of the terms. The GCF is 4.
Step 3: Factor out the GCF (4) from the expression. This gives us 4(x^2 - 4).
Step 4: Now, look at the expression inside the parentheses: x^2 - 4.
Step 5: Recognize that x^2 - 4 is a difference of squares, which can be factored as (x - 2)(x + 2).
Step 6: Substitute back the factored form into the expression. So, we have 4(x - 2)(x + 2).
Step 7: The complete factorization of the original expression is 4(x - 2)(x + 2).

Factoring Quadratic Expressions – The process of breaking down a quadratic expression into simpler factors, often involving finding the greatest common factor and recognizing special products like the difference of squares.
Greatest Common Factor (GCF) – Identifying and factoring out the largest factor common to all terms in the expression.
Difference of Squares – Recognizing and applying the formula a^2 - b^2 = (a - b)(a + b) to factor expressions that fit this pattern.

Factor the expression 4x^2 - 16.

What’s inside this PDF?

Factor the expression 4x^2 - 16.

Practice Questions

Questions & Step-by-Step Solutions

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