ScoreReady SAT
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Score band 700-800 · Passport to Advanced Math

Polynomial Operations drills for 700-800

400500600700800

Targeted practice for students currently scoring in the 700-800 range, drilling exclusively on polynomial operations.

What a 700-800 scorer needs from this topic

The 700 to 800 band is the elite tier of SAT Math. Reaching it requires zero careless errors and confident solves on the hardest one or two questions in each module. Mastery-band drills focus on the hardest released questions: multi-concept problems that combine two or three skills in one stem, abstract algebraic manipulation with parameters instead of numbers, geometry questions that require a clever construction, and data-analysis questions that test conceptual understanding rather than computation. At this level, speed matters as much as accuracy, because the only way to leave time for the hardest questions is to dispatch the easy and medium ones in well under a minute each.

For Polynomial Operations specifically, students in the 700-800 band need to focus on the question patterns the College Board uses at this difficulty level. Add, multiply, and factor polynomial expressions. The questions below are pulled from the ScoreReady question bank and filtered to the 700-800 band based on difficulty calibration that matches publicly released College Board practice materials.

Drill these untimed first. Once you can produce a clean worked solution on paper for every question without notes, switch to timed mode and aim for under 75 seconds per question. That pace is roughly the average time per question on the actual SAT Math section, and it leaves time for the harder questions you will see at the end of each module.

Practice set

  1. 700-800 hard Remainder and Factor Theorems

    Which expression is equivalent to 5x + 44x + 4?

    1. A 20x^2 + 36x + 16
    2. B 20x^2 + 16x + 16
    3. C 21x^2 + (36)x + (16)
    4. D 20x^2 + 20x + 16
    Worked solution

    Answer: A — 20x^2 + 36x + 16

    Use FOIL. First: (5x)(4x) = 20x^2. Outer: (5x)(4) = 20x. Inner: (4)(4x) = 16x. Last: (4)(4) = 16. Combine the middle terms: 20 + 16 = 36. The product is 20x^2 + (36)x + (16).

  2. 700-800 hard Multiplying Polynomials

    Which expression is equivalent to 2x - 11x - 5?

    1. A 2x^2 - 11x + 5
    2. B 2x^2 + -10x + 5
    3. C 3x^2 + (-11)x + (5)
    4. D 2x^2 + -1x + 5
    Worked solution

    Answer: A — 2x^2 - 11x + 5

    Use FOIL. First: (2x)(1x) = 2x^2. Outer: (2x)(-5) = -10x. Inner: (-1)(1x) = -1x. Last: (-1)(-5) = 5. Combine the middle terms: -10 + -1 = -11. The product is 2x^2 + (-11)x + (5).

  3. 700-800 hard Factoring Higher-Degree Polynomials

    Which expression is equivalent to 2x + 21x - 6?

    1. A 2x^2 + -12x + -12
    2. B 2x^2 + 2x + -12
    3. C 2x^2 - 10x - 12
    4. D 3x^2 + (-10)x + (-12)
    Worked solution

    Answer: C — 2x^2 - 10x - 12

    Use FOIL. First: (2x)(1x) = 2x^2. Outer: (2x)(-6) = -12x. Inner: (2)(1x) = 2x. Last: (2)(-6) = -12. Combine the middle terms: -12 + 2 = -10. The product is 2x^2 + (-10)x + (-12).

  4. 700-800 hard Polynomial Long and Synthetic Division

    Which expression is equivalent to 3x + 12x + 6?

    1. A 6x^2 + 2x + 6
    2. B 7x^2 + (20)x + (6)
    3. C 6x^2 + 20x + 6
    4. D 6x^2 + 18x + 6
    Worked solution

    Answer: C — 6x^2 + 20x + 6

    Use FOIL. First: (3x)(2x) = 6x^2. Outer: (3x)(6) = 18x. Inner: (1)(2x) = 2x. Last: (1)(6) = 6. Combine the middle terms: 18 + 2 = 20. The product is 6x^2 + (20)x + (6).

  5. 700-800 hard Remainder and Factor Theorems

    Which expression is equivalent to 5x - 23x + 5?

    1. A 15x^2 + -6x + -10
    2. B 15x^2 + 19x - 10
    3. C 15x^2 + 25x + -10
    4. D 16x^2 + (19)x + (-10)
    Worked solution

    Answer: B — 15x^2 + 19x - 10

    Use FOIL. First: (5x)(3x) = 15x^2. Outer: (5x)(5) = 25x. Inner: (-2)(3x) = -6x. Last: (-2)(5) = -10. Combine the middle terms: 25 + -6 = 19. The product is 15x^2 + (19)x + (-10).

  6. 700-800 hard Multiplying Polynomials

    Which expression is equivalent to 1x - 62x - 4?

    1. A 2x^2 - 16x + 24
    2. B 2x^2 + -12x + 24
    3. C 3x^2 + (-16)x + (24)
    4. D 2x^2 + -4x + 24
    Worked solution

    Answer: A — 2x^2 - 16x + 24

    Use FOIL. First: (1x)(2x) = 2x^2. Outer: (1x)(-4) = -4x. Inner: (-6)(2x) = -12x. Last: (-6)(-4) = 24. Combine the middle terms: -4 + -12 = -16. The product is 2x^2 + (-16)x + (24).

How to use these drills to climb a band

Climbing from one score band to the next requires a different study mix than climbing within a band. Within a band, you are mostly fixing careless errors and pattern-recognizing the question types you already understand. Climbing to the next band means adding new question types to your toolbox — patterns you currently recognize but cannot solve fluently. The 700–800 set in this drill is exactly that toolbox for students currently in the 600–700 range.

The single most reliable indicator that you are ready to move up a band is being able to explain a worked solution to someone else, in your own words, without referring to notes. Practice this with one classmate or one parent per week. The act of teaching exposes the gaps your timed solves did not.

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