Factor the polynomial 3x^2 - 12.

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Question: Factor the polynomial 3x^2 - 12.

Options:

Correct Answer: 3(x - 4)(x + 4)

Solution:

First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, factor x^2 - 4 as a difference of squares: 3(x - 2)(x + 2).

Factor the polynomial 3x^2 - 12.

Factor the polynomial 3x^2 - 12.

Step 1: Look at the polynomial 3x^2 - 12 and find the greatest common factor (GCF). The GCF is 3.
Step 2: Factor out the GCF (3) from the polynomial. This gives us 3(x^2 - 4).
Step 3: Now, look at the expression inside the parentheses, which is x^2 - 4. This is a difference of squares.
Step 4: Factor the difference of squares x^2 - 4 into (x - 2)(x + 2).
Step 5: Combine everything together. The final factored form is 3(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.
Greatest Common Factor (GCF) – The largest factor that divides all terms of the polynomial, which can be factored out to simplify the expression.
Difference of Squares – A specific factoring technique used for expressions in the form a^2 - b^2, which factors into (a - b)(a + b).