leroy.marshall
leroy.marshall 2d ago โ€ข 0 views

Factoring quadratics examples

Hey there! ๐Ÿ‘‹ Factoring quadratics can seem tricky, but with a little practice, you'll be a pro in no time. Check out this quick guide and quiz to boost your skills! ๐Ÿงฎ
๐Ÿงฎ Mathematics

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wesley_gomez Dec 31, 2025

๐Ÿ“š Quick Study Guide

    ๐Ÿ” Factoring is the process of breaking down a quadratic expression into its constituent binomial factors.
    ๐Ÿ’ก A quadratic expression is of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.
    ๐Ÿ“ The goal is to find two binomials $(px + q)$ and $(rx + s)$ such that $(px + q)(rx + s) = ax^2 + bx + c$.
    โž• If $a = 1$, we look for two numbers that add up to $b$ and multiply to $c$.
    โž— For example, to factor $x^2 + 5x + 6$, we need two numbers that add to 5 and multiply to 6 (2 and 3).
    โœ… Thus, $x^2 + 5x + 6 = (x + 2)(x + 3)$.
    โญ When $a \neq 1$, use techniques like factoring by grouping.

Practice Quiz

  1. What are the factors of $x^2 + 7x + 12$?
    1. (x + 1)(x + 12)
    2. (x + 2)(x + 6)
    3. (x + 3)(x + 4)
    4. (x + 1)(x + 7)
  2. Factor $x^2 - 5x + 6$.
    1. (x - 1)(x - 6)
    2. (x - 2)(x - 3)
    3. (x + 2)(x + 3)
    4. (x + 1)(x + 6)
  3. Factor $x^2 + 2x - 8$.
    1. (x + 4)(x - 2)
    2. (x - 4)(x - 2)
    3. (x + 4)(x + 2)
    4. (x - 4)(x + 2)
  4. What are the factors of $2x^2 + 5x + 2$?
    1. (2x + 1)(x + 2)
    2. (2x + 2)(x + 1)
    3. (x + 1)(x + 2)
    4. (2x - 1)(x - 2)
  5. Factor $3x^2 - 10x + 3$.
    1. (3x - 1)(x - 3)
    2. (3x + 1)(x + 3)
    3. (3x - 3)(x - 1)
    4. (3x + 3)(x + 1)
  6. What are the factors of $x^2 - 9$?
    1. (x - 3)(x - 3)
    2. (x + 3)(x + 3)
    3. (x + 3)(x - 3)
    4. (x - 9)(x + 1)
  7. Factor $4x^2 - 4x + 1$.
    1. (2x + 1)(2x + 1)
    2. (2x - 1)(2x - 1)
    3. (2x + 1)(2x - 1)
    4. (4x - 1)(x - 1)
Click to see Answers
  1. C
  2. B
  3. A
  4. A
  5. A
  6. C
  7. B

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