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Answer:
[tex](x+2)(x+3)[/tex]
Step-by-step explanation:
Factoring by grouping is a method used to grab outside factors of a certain expression and combining them with the inside factors to factor the whole polynomial.
Solving:
[tex]\subsection*{}For \( x^2 + 5x + 6 \), we have:\[a = 1, \quad b = 5, \quad c = 6\][/tex]
[tex]\text{Multiply a and c}[/tex]
[tex]\[a \cdot c = 1 \cdot 6 = \boxed{6}\][/tex]
[tex]\subsection*{ Rewrite the Middle Term:}\[x^2 + 5x + 6 = \boxed{x^2 + 2x + 3x + 6}\][/tex]
[tex]\subsection*}Group the terms in pairs:\[(x^2 + 2x) + (3x + 6)\][/tex]
[tex]\text{Factor:}\\\\\[x(x + 2) + 3(x + 2)\][/tex]
[tex]\text{Combine:}\\\\\[(x + 2)(x + 3)\][/tex]
Therefore, the factored form of [tex]x^2+5x+20[/tex] is [tex](x+2)(x+3)[/tex]