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Factor. $\newline$ $2h^2 + 13h + 11$

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Factor quadratics with other leading coefficients

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Q. Factor.

\newline

2h^2 + 13h + 11

Identify coefficients: Identify the coefficients of the quadratic expression. $\newline$ The quadratic expression is in the form $ax^2 + bx + c$ , where $a$ , $b$ , and $c$ are constants. For the expression $2h^2 + 13h + 11$ , we have: $\newline$ $a = 2$ $\newline$ $b = 13$ $\newline$ $c = 11$
Find numbers for $ac$ : Find two numbers that multiply to $ac$ ( $a$ times $c$ ) and add up to $b$ . We need to find two numbers that multiply to $(2 \times 11) = 22$ and add up to $13$ . The numbers that satisfy these conditions are $2$ and $11$ because: $2 \times 11 = 22$ $ac$ $0$
Rewrite middle term: Rewrite the middle term of the quadratic expression using the two numbers found. $\newline$ We can express $13h$ as the sum of $2h$ and $11h$ . So, the expression $2h^2 + 13h + 11$ can be rewritten as: $\newline$ $2h^2 + 2h + 11h + 11$
Factor by grouping: Factor by grouping. $\newline$ We group the terms as follows: $\newline$ $(2h^2 + 2h) + (11h + 11)$ $\newline$ Now, factor out the common factors from each group: $\newline$ $2h * (h + 1) + 11 * (h + 1)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ Both groups contain the common factor $(h + 1)$ , so we can factor this out: $\newline$ $(2h + 11)(h + 1)$

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