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DEMO: Solving by factoring

Worked examples

• $x^2 - 7x + 12 = 0 \Rightarrow (x - 3)(x - 4) = 0 \Rightarrow x = 3$ or $x = 4$.
• $x^2 + 2x - 8 = 0 \Rightarrow (x + 4)(x - 2) = 0 \Rightarrow x = -4$ or $x = 2$.
• $x^2 - 16 = 0 \Rightarrow (x - 4)(x + 4) = 0 \Rightarrow x = 4$ or $x = -4$.

Key points

• Find two numbers that multiply to $6$ and add to $-5$.
• $-2$ and $-3$ work, so $(x - 2)(x - 3) = 0$.
• Find two numbers that multiply to $-12$ and add to $1$.
• $4$ and $-3$ work, so $(x + 4)(x - 3) = 0$.
• This is a difference of squares: $a^2 - b^2 = (a - b)(a + b)$.
• $(x - 3)(x + 3) = 0$.

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