Algebra Question of the Day

1. $x+4x-2$
2. $x,\ 4,\ x,\ -2$
3. $(x+4)\ \text{and}\ (x-2)$ (correct answer)
4. $x+4,\ x,\ -2$

Explanation: This question tests your understanding of the parts of algebraic expressions—specifically, how to identify factors. Factors are parts of an expression that are multiplied together: when you see multiplication (either with · or parentheses next to each other), you're looking at factors. For example, in 4(x + 3), the factors are 4 and (x + 3) because they're being multiplied. In (x + 4)(x - 2), we can see what's being multiplied together: it's (x + 4) times (x - 2). This means the factors are (x + 4) and (x - 2). Remember, factors are connected by multiplication, while terms are connected by addition and subtraction. Choice A is correct because it properly identifies the factors as (x + 4) and (x - 2), following the definition that factors are the multiplied parts. You've got it! Choice B is close, but it confuses terms with factors: it lists x, 4, x, -2 which are terms inside the parentheses, but the question asks for the main factors. Remember: terms are added/subtracted, factors are multiplied! Think of terms as 'ingredients being added together' and factors as 'ingredients being multiplied together.' In (x + 4)(x - 2), you're multiplying (x + 4) times (x - 2), so those are factors. But when you expand to x² + 2x - 8, you're adding x², 2x, and -8, so those are terms. Choice D treats parts inside parentheses as separate terms, but actually (x + 4) is grouped as one factor here. Terms are only separated by + and - at the outermost level!