Algebraic Factorization and Quadratic Word Problem Review

Vocabulary flashcards covering key terms, mathematical values, and algebraic factorization concepts from the lecture notes.

Length of the pool

$12\,\text{metres}$, which is the positive root $x = 12$ obtained from solving $x^2 - 4x - 96 = 0$.

Breadth of the pool

$8\,\text{metres}$, calculated using the formula $x - 4 = 12 - 4 = 8\,\text{metres}$.

Ignored root $x = -8$

The negative solution to $x^2 - 4x - 96 = 0$, which is discarded because the length of the pool cannot be negative.

Factored form of $x^2 - 4x - 96$

$$(x - 12)(x + 8)$$

Splitting of the middle term $-4x$

Decomposing $-4x$ into $-12x + 8x$ using the factors $-12$ and $8$, since $(-12) \times 8 = -96$ and $(-12) + 8 = -4$.