Question

(p+5power2)+2(p+5)
Factorize the following algebraic expression:
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Answer 1

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$\huge{\blue{\boxed{\boxed{\boxed{\pink{\underline{\underline{\mathfrak{\red{❤Answer❤}}}}}}}}}}$

$\: \red\bigstar \displaystyle \bf{(p + 5 {p}^{2} ) + 2(p + 5) = 0}...given \: equation$

$\: \ \\ \implies \displaystyle \sf{(p + 5 {p}^{2} ) + 2(p + 5) = 0}$

$\: \: \\ \implies \displaystyle \sf{(p + {5p}^{2} ) + 2p + 5 = 0}$

$\: \: \\ \implies \displaystyle \sf{(5 {p}^{2} + p + 2p + 10 )= 0}$

$\: \: \: \\ \implies \displaystyle \sf{ {5p}^{2} + 3p + 10 = 0}$

$\: \: \\ \red\bullet \underline{\bf{by \: usin g \: formula \: method}}$

$\: \\ \implies \displaystyle \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }$

$\: \: \\ \implies \underline{\displaystyle \bf{substiute \: the \: values \to \: a = 5 \: \: b = 3 \: and \: c = 10}}$

$\: \: \\ \implies \displaystyle \sf{x = \frac{ - 3 \pm \sqrt{ {3}^{2} - 4(5)(10) } }{2 \times 5} }$

$\: \: \\ \implies \displaystyle \sf{x = \frac{ - 3 \pm \sqrt{9 - 200} }{10} }$

$\\ \: \implies \displaystyle \sf{x = \frac{ - 3 \pm \sqrt{- 191}}{10} }$

$\: \: \\ \implies \displaystyle \sf{x = \frac{ - 3 + \sqrt{191} }{10} \: and \: x = \frac{ - 3 - \sqrt{191} }{10} }$