Question

(3p^2 + 17p + 10) = (p + 5)​

Answer 1

$\huge\tt\underline\red{Ans}\underline {w}\underline\purple{er}\underline{:}\orange {\:\:p=\frac{-1}{3}}$

$\huge \underbrace \mathfrak \red{\bigstar Explanation}$

$\tt {Qn. }\mathfrak{(3p^2 + 17p + 10) = (p + 5) }$

$\tt Sol:⟹\mathfrak{(3p^2 + 17p + 10) = (p + 5) }$

$⟹\mathfrak{(3p^2 + 15p+2p + 10) = (p + 5) }$

$⟹\mathfrak{[3p(p+ 5)+2(p + 5)] = (p + 5) }$

$⟹\mathfrak{(3p+2)(p + 5)= (p + 5) }$

$⟹\mathfrak{(3p+2)=\frac{(p+5)} {(p + 5)} }$

$⟹\mathfrak{(3p+2)=\frac{\cancel{(p+5)}} {\cancel{(p + 5)}}}$

$⟹\mathfrak{3p+2=1}$

$⟹\mathfrak{3p=1-2}$

$Ans ⟹\mathfrak{p=\frac{-1}{3}}$

Answer 2

$here \: is \: your \: solution \: -$

$☞( {3p}^{2} + 17p + 10) = (p + 5) \\ \\☞ by \: middle \: term \: splitting \: \\☞ (3 {p}^{2} + 15p + 2p + 10) = \:( p + 5) \\ \\ ☞ = {3p(p + 5) + 2( p + 5) } = (p + 5) \\ \\ ☞ = (3p + 2)(p + 5) = \: (p + 5) \\ \\☞ (3p + 2) = \frac{(p + 5)}{(p + 5)} \\ \\ ☞(3p + 2) = 1 \\ \\ ☞3p + 2 = 1 \\ \\ ☞3p = 1 - 2 \\ \\ ☞3p = - 1 \\ \\ ☞ p = \frac{ - 1}{3}$

Answer = -1/3