courses › Algebra

Expand, factor, and use the remainder theorem.

Pen and paper is fine · no calculator needed why?

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Opens at level 26.

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Builds on: Linear equations (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Expand brackets par 16 s not tried yet

  worked example

  Expand (x + 1)(x − 7). What is the coefficient of x?

  Answer: -6

  1. Outer: x × (−7) = −7x. Inner: 1 × x = x.
  2. Add them: the coefficient of x is −7 + 1 = −6.
  3. Full expansion: x² − 6x − 7.

• Factor a trinomial par 20 s not tried yet

  worked example

  x² − 17x + 70 = (x − a)(x − b) with a < b. Enter a, b.

  Answer: (7, 10)

  1. Find two numbers that multiply to 70 and add to 17: 7 and 10.
  2. So x² − 17x + 70 = (x − 7)(x − 10).

• Remainder theorem par 18 s not tried yet

  worked example

  What is the remainder when 2x³ + 3x² + 3x + 2 is divided by x − 1?

  Answer: 10

  1. Call the polynomial p(x). By the remainder theorem, the remainder is p(1).
  2. p(1) = 2 × 1³ + 3 × 1² + 3 × 1 + 2 = 2 + 3 + 3 + 2 = 10.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

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