This question tests your understanding of the structure of algebraic expressions—specifically, distinguishing terms (additive parts) from factors (multiplicative parts within a term). Terms are separated by + or -, so in 2x(x-3)² + 5, there are two terms: 2x(x-3)² and +5, treating the parenthetical as a unit. Factors within the first term are 2, x, and (x-3)², since they're multiplied together—note that (x-3)² is one factor, even though it's (x-3)*(x-3) inside. Coefficients are numerical multipliers, like 2 here, but we're identifying terms and factors. Remember, don't expand unless told to; keep groups intact for term counting! Choice B correctly identifies the two terms and the factors of the first term by keeping the multiplied parts together but listing them separately as factors. Choice A is a tempting distractor because it treats 2x and (x-3)² as separate terms, but there's no + or - between them—it's multiplication, so one term! For transferable strategy, first count terms by + and - separators (here, one + , so two terms), then for factors in a term, list what's multiplied: like in a b (c+d), factors are a, b, (c+d). You're doing fantastic—keep practicing, and it'll become second nature!

This question tests your understanding of the structure of algebraic expressions—specifically, identifying terms without expanding, treating multiplied groups as single terms. Terms are separated by + or -: in 5(x-1)² + 2x(x+3) - 4, they are 5(x-1)², +2x(x+3), and -4—three terms, keeping parentheses intact. Signs belong to terms, so positive first, positive second, negative third. Factors are within terms, like 5 and (x-1)² in the first, but the question asks for terms, not factors or coefficients. Don't break squares or products into more terms unless there's + or - inside! Choice B correctly identifies the three terms by grouping the multiplied parts correctly. Choice A is a tempting distractor because it lists factors like 5 and (x-1)² as separate terms, but multiplication doesn't create new terms—only addition/subtraction does. Strategy: count + and - signs (two here: + and -), add 1 for the first term, getting three; list each cluster between them. You're doing brilliantly—keep shining!

This question tests your understanding of the structure of algebraic expressions—specifically, how to identify coefficients, which are the numerical multipliers of variable parts in a term. Coefficients are the numerical factors in each term: in 7x³ - 5x² + 2x - 1, the coefficient of x³ is 7, of x² is -5, of x is 2, and the constant term is -1 (which is like -1 times x⁰). Remember, the sign is part of the coefficient, so -5x² means the coefficient is -5, not just 5 with a minus sign separate. Terms are separated by + or -, but here we're honing in on the coefficient of a specific power, x². In this polynomial, the x² term is -5x², so its coefficient is -5—easy to spot once you include the sign! Choice A correctly identifies the coefficient as -5 by recognizing the negative sign as part of it. Choice B is a tempting distractor because it ignores the sign and picks the absolute value 5, but remember, coefficients include signs—think of it as the number you'd pull out when factoring! To find coefficients quickly, rewrite the expression with all signs attached to the numbers: 7x³ + (-5)x² + 2x + (-1), and you'll never miss one. You're doing awesome at this—keep building that polynomial intuition!

This question tests your understanding of the structure of algebraic expressions—specifically, how to identify terms, which are the parts separated by addition or subtraction signs. Terms are the pieces of an expression separated by plus or minus signs: in 4x² - 3x + 9, there are three terms—4x², -3x, and +9 (we include the sign with each term after the first). The sign belongs to the term, so even though it's written as -3x + 9, it's 4x² plus negative 3x plus 9. Factors are parts multiplied together within a term, but here we're focusing on terms, not factors or coefficients. In this expression, the terms are correctly identified as 4x², -3x, and 9, making three terms total—remember, constants like 9 are terms too! Choice B correctly identifies the three terms by properly distinguishing the additive parts and including their signs. Choice A is a tempting distractor because it splits -3x into -3 and x, but that's confusing factors with terms— -3x is one term, where -3 is the coefficient and x is the variable factor. To count terms reliably, look at the expression and identify each complete piece between the + and - signs, always attaching the sign to the following term; for example, in ax + by - cz, the terms are ax, +by, -cz. Keep practicing this, and you'll get great at breaking down polynomials—you've got this!

This question tests your understanding of the structure of algebraic expressions—specifically, how to identify terms without expanding grouped factors. Terms are the pieces separated by plus or minus signs: in 3(x+2)² + 5x - 1, the terms are 3(x+2)², +5x, and -1, treating the parenthetical part as a single unit since it's not expanded. The sign belongs to the term, so we have a positive first term, positive 5x, and negative 1. Factors are parts multiplied within a term, like in 3(x+2)², where 3 and (x+2)² are factors, but the question asks for terms, not factors. There are three terms here—don't break down the multiplied parts into separate terms unless there's a + or - between them! Choice B correctly identifies the three terms by keeping the multiplied groups intact. Choice A is a tempting distractor because it lists the factors as if they were terms, like separating 3 from (x+2)², but remember, multiplication doesn't separate terms—only + and - do! When dealing with unexpanded expressions, treat each multiplied cluster between + and - as one term; for example, in a(b+c) - d, there are two terms: a(b+c) and -d. Great job tackling this—you're getting sharper with every question!

This question tests your understanding of the structure of algebraic expressions—specifically, listing terms and their coefficients, where terms include signs and coefficients are the numerical parts. Terms are separated by + or -: in -x³ + (2/3)x - 8, they are -x³, +(2/3)x, and -8, with coefficients -1 (for -x³ = -1 * x³), 2/3 (for (2/3)x), and -8 (for the constant, like -8 * 1). The sign belongs to the term, so the first term is negative, even though there's no explicit + before it. Factors are within terms, but here we're pairing each term with its coefficient. Constants have coefficients too— -8 is the coefficient of the invisible x⁰ = 1! Choice B correctly lists the terms with signs and their coefficients by properly attaching signs and recognizing implicit 1 or -1. Choice A is a tempting distractor because it makes the first term positive x³ with coefficient 1, but the expression starts with -x³, so the term is negative with coefficient -1. For strategy, always include the leading sign with the first term if it's negative, and for coefficients, factor out the number: like -x³ = (-1)x³. You're excelling at this—stay confident!

This question tests your understanding of the structure of algebraic expressions—specifically, identifying the coefficient of a specific variable term like xy² in 2xy² - 3x²y + 5y. Coefficients are the numerical multipliers: the term 2xy² has coefficient 2 (multiplying xy²), -3x²y has -3 (for x²y), and 5y has 5 (for y)—we pick the one matching xy². Terms are the additive parts: 2xy², -3x²y, +5y, each with its coefficient including the sign. Factors within a term would be like 2, x, y² for the first, but we're after the coefficient of a particular monomial. Remember, even if variables are similar, we match exactly—xy² is different from x²y! Choice A correctly identifies 2 as the coefficient by spotting the matching term 2xy². Choice B is a tempting distractor because it includes the y², but that's part of the variable, not the coefficient—coefficients are just the numbers! To find a specific coefficient, scan for the exact variable combo and grab its numerical multiplier, including sign; for example, in ax² + bxy + cy, coefficient of xy is b. You're nailing this—keep up the great effort!

This question tests your understanding of the structure of algebraic expressions—specifically, identifying terms in the numerator of a rational expression, treating it like a standalone polynomial. Terms are pieces separated by + or -: in the numerator 3x² - 2x + 5, there are three terms—3x², -2x, and +5, with signs included. The denominator doesn't affect the numerator's terms; we focus only on the top. Factors are multiplicative within terms, but here we're just listing the numerator's terms. Remember, even in fractions, terms are defined the same way—don't divide or simplify unless asked! Choice A correctly identifies the three terms with their signs by treating the numerator as a polynomial. Choice D is a tempting distractor because it drops the negative sign on -2x, but remember, signs are part of terms—it's -2x, not +2x! To spot terms in any expression, ignore denominators or other structures and just look for + and - in the part you're analyzing; for example, in (a + b - c)/d, numerator terms are a, +b, -c. Awesome work—you're building strong skills here!

This question tests your understanding of the structure of algebraic expressions—specifically, how to identify factors within a single term, which are the parts connected by multiplication. Factors are the pieces multiplied together in a term: in -6x²y, they are -6, x², and y (or you could break x² into x and x, but typically we keep powers intact unless specified). The coefficient is the numerical part, here -6, but the question focuses on all factors, including variables. Terms are additive parts, but this is one term, so we're breaking it down multiplicatively. Remember, the negative sign is part of the numerical factor, not a separate piece! Choice C correctly lists the factors as -6, x², y by properly identifying the multiplied components. Choice A is a tempting distractor because it breaks x² into x but incorrectly says 'x² counts as x'—no, x² is a distinct factor (x*x), but we list it as x² for simplicity. To identify factors, rewrite the term as a product: -6 * x² * y, and list each multiplier—that's your list! You're mastering this concept—keep going, you're unstoppable!

This question tests your understanding of implicit coefficients, especially with negative signs. Coefficients include implied 1 or -1 when no number is written; for instance, x means 1x, and -x means -1x. In -x + 7, the term -x is -1 times x, so the coefficient of x is -1—the negative sign is part of the coefficient. Choice A correctly identifies -1 by recognizing the implicit multiplication. A tempting distractor like Choice B might ignore the negative, picking 1, but always incorporate the sign into the coefficient. Remember the rewrite trick: -x = -1 · x, making it obvious. You're getting stronger at spotting these details—excellent effort!