Question

warm - up: factor each completely

1. $x^{2}-7x - 18$
2. $p^{2}-5p - 14$
3. $m^{2}-9m + 8$
4. $x^{2}-16x + 63$

friday

Explanation:

Step1: Factor \(x^{2}-7x - 18\)

Find two numbers that multiply to \(-18\) and add to \(-7\). The numbers are \(-9\) and \(2\). So \(x^{2}-7x - 18=(x - 9)(x+2)\)

Step2: Factor \(p^{2}-5p - 14\)

Find two numbers that multiply to \(-14\) and add to \(-5\). The numbers are \(-7\) and \(2\). So \(p^{2}-5p - 14=(p - 7)(p + 2)\)

Step3: Factor \(m^{2}-9m + 8\)

Find two numbers that multiply to \(8\) and add to \(-9\). The numbers are \(-8\) and \(-1\). So \(m^{2}-9m + 8=(m - 8)(m - 1)\)

Step4: Factor \(x^{2}-16x + 63\)

Find two numbers that multiply to \(63\) and add to \(-16\). The numbers are \(-9\) and \(-7\). So \(x^{2}-16x + 63=(x - 9)(x - 7)\)

Answer:

1. \((x - 9)(x + 2)\)
2. \((p - 7)(p + 2)\)
3. \((m - 8)(m - 1)\)
4. \((x - 9)(x - 7)\)