Question

Factorize the following expression using the algebraic expression:
${x}^{2} + x + \frac{1}{4}$
​

Answer 1

Step-by-step explanation:

→In general, given $\bf a{x}^{2}+bx+c$, the factored form is:

$\tt\quad\bull\qquad a\bigg(x-\dfrac{-b+\sqrt{{b}^{2}-4ac}}{2a} \bigg) \bigg(x-\dfrac{-b-\sqrt{{b}^{2}-4ac}}{2a}\bigg)$

→In this case, a=1, b=1 and $\tt c=\frac{1}{4}$

$\tt \quad \bull \qquad \bigg(x-\dfrac{-1+\sqrt{1-4\times \frac{1}{4}}}{2} \bigg) \bigg(x-\dfrac{-1-\sqrt{1-4\times \frac{1}{4}}}{2} \bigg)$

Simplify.

$\tt \quad \bull \qquad \bigg(x+\dfrac{1}{2}\bigg)\bigg(x+\dfrac{1}{2}\bigg)$

→ Use Product Rule: $\tt{x}^{a}{x}^{b}={x}^{a+b}$

$\boxed{ \xcancel{ \boxed{ \tt \quad \bull \quad}}{ \tt \bigg(x+\frac{1}{2} \bigg)}^{2}}$