Question
Factorize: $\text{x}^2+\frac{12}{35}\text{x}+\frac{1}{35}$
✓
Answer
$\text{x}^2+\frac{12}{35}\text{x}+\frac{1}{35}$ Splitting the middle term, $=\text{x}^2+\frac{5}{35}\text{x}+\frac{7}{35}\text{x}+\frac{1}{35}$
$\Big[\therefore\frac{12}{35}=\frac{5}{35}+\frac{7}{35} \ \text{and} \ \frac{5}{35}\times\frac{7}{35}=\frac{1}{35}\Big]$
$=\text{x}^2+\frac{\text{x}}{7}+\frac{\text{x}}{5}+\frac{1}{35}$
$=\text{x}\Big(\text{x}+\frac{1}{7}\Big)+\frac{1}{5}\Big(\text{x}+\frac{1}{7}\Big)$
$=\Big(\text{x}+\frac{1}{7}\Big)\Big(\text{x}+\frac{1}{5}\Big)$
$\therefore\text{x}^2+\frac{12}{35}\text{x}+\frac{1}{35}=\Big(\text{x}+\frac{1}{7}\Big)\Big(\text{x}+\frac{1}{5}\Big)$
$\Big[\therefore\frac{12}{35}=\frac{5}{35}+\frac{7}{35} \ \text{and} \ \frac{5}{35}\times\frac{7}{35}=\frac{1}{35}\Big]$
$=\text{x}^2+\frac{\text{x}}{7}+\frac{\text{x}}{5}+\frac{1}{35}$
$=\text{x}\Big(\text{x}+\frac{1}{7}\Big)+\frac{1}{5}\Big(\text{x}+\frac{1}{7}\Big)$
$=\Big(\text{x}+\frac{1}{7}\Big)\Big(\text{x}+\frac{1}{5}\Big)$
$\therefore\text{x}^2+\frac{12}{35}\text{x}+\frac{1}{35}=\Big(\text{x}+\frac{1}{7}\Big)\Big(\text{x}+\frac{1}{5}\Big)$
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