Factor the polynomial 2x^2 - 8.

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Question: Factor the polynomial 2x^2 - 8.

Options:

Correct Answer: 2(x - 4)(x + 4)

Solution:

Factor out the common term 2: 2(x^2 - 4) = 2(x - 2)(x + 2).

Factor the polynomial 2x^2 - 8.

Factor the polynomial 2x^2 - 8.

Step 1: Look at the polynomial 2x^2 - 8 and identify the common factor in both terms.
Step 2: The common factor is 2. Factor out 2 from the polynomial: 2(x^2 - 4).
Step 3: Now, look at the expression inside the parentheses: x^2 - 4. This is a difference of squares.
Step 4: Recall that a difference of squares can be factored using the formula a^2 - b^2 = (a - b)(a + b).
Step 5: In this case, x^2 - 4 can be written as (x - 2)(x + 2) because 4 is 2^2.
Step 6: Combine the factored common term with the factored difference of squares: 2(x - 2)(x + 2).

Factoring Polynomials – The process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.
Difference of Squares – A specific factoring technique used for expressions of the form a^2 - b^2, which factors into (a - b)(a + b).
Common Factor Extraction – Identifying and factoring out the greatest common factor from all terms in a polynomial.