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Explore Binomial Theorem and Polynomial Factoring with 10 Daily Math Challenges

Dive into a series of 10 daily math challenges designed to reinforce your understanding of the binomial theorem, polynomial factoring, and algebraic expressions. Each day presents tasks that will require applying concepts such as finding values using Pascal's triangle, solving for expressions, and simplifying complex equations. Perfect for students looking to sharpen their math skills and enhance their problem-solving abilities. Join us in unraveling the mysteries of algebra, one challenge at a time!

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Explore Binomial Theorem and Polynomial Factoring with 10 Daily Math Challenges

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  1. Daily 10 Day 1

  2. 1. Find the value of (x + 2)4 using Pascal’s triangle and the binomial theorem. • 4x4 – 6x3 – 4x2 + 8x + 16 • x4 – 30x3 – 16x2 + 56x • x4 + 8x3 + 24x2 + 32x + 16 • x4 + 8x + 16

  3. 2. The volume of a rectangular prism is V= -2n3 – 8n2 + 10n. The height of the prism is h = -2n. Find the dimensions (length and width) of the base of the prism? A. (n – 5)(n + 1) B. (n + 5)(n – 1) C. (n + 2)(n + 3) D. (n – 2)(n – 3)

  4. Answers: • C MM1A2.d, level 1 • B MM1A2.g, level 2

  5. Daily 10 Day 2

  6. 1. Which is one of the correct factors of:x2 – 3x – 28? A. (x + 7) B. (x + 2) C. (x + 4) D. (x – 14)

  7. 2. If the area of a square is A=x2 + 10x + 25, find its perimeter. • x + 5 • 4x2 + 40x + 100 • 4x + 20 • 2x + 10

  8. Answers: • C MM1a2.f, level 1 • C MM1A2.g, level 2

  9. Daily 10 Day 3

  10. 1. Which expression is equivalent to12x5 + 15x3 – 27x 3x ? A. 4x5 + 5x2 – 9x B. (2x2 – 3)(2x2 + 3) C. 9x5 + 12x2 – 24x D. 4x4 + 5x2 – 9

  11. 2. Find the value of the second term of (x – y)5 using Pascal’s triangle and the binomial theorem. • 10x5 • -5x4 y • 5x4 y • -10xy4

  12. Answers: • D MM1A2.c, level 1 • B MM1A2.d, level 2

  13. Daily 10 Day 4

  14. 1. Which is the completely factored form of 3x3 – 12x + 2x2 – 8 ? • (3x + 2)(x2 – 4) • (3x – 12)(2x – 8) • (3x + 2)(x - 2)(x + 2) • 3x(x2 – 4) + 2(x2 – 4)

  15. x + y • A = 2x + 2(x + y) • A = x2 + (x + y)2 • A = 2x(x + y) • A = x(x + y) x

  16. Answers: • C MM1a2.f, level 1 • D MM1A2.g, level 1

  17. Daily 10 Day 5

  18. 1. Simplify. x2 + 3x – 18 x2 - 9 • x + 2 • x + 6 x + 3 • x + 6 x – 3 • 3x - 2

  19. Subtract:(4x3 – 12x2 + 9x – 4) – (x3 – 3x + 9) • 5x3 – 15x2 + 18x – 4 • 3x3 – 12x2 + 12x – 13 • 5x3 – 15x2 + 18x – 4 • 4 – 12x2 + 6x + 5

  20. Answers: • C MM1A2.c, level 1 • B MM1a2.c, level 1

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