Factor Quadratic Trinomials with Leading Coefficient Other than 1: exemplo 7.31

Use the preliminary strategy.

$\begin{array}{cccc}\text{Is there a greatest common factor?}\hfill & & & 4y^2-36y+56\hfill \\ \text{Yes, GCF = 4. Factor it.}\hfill & & & 4\left(y^2-9y+14\right)\hfill \\ \text{Inside the parentheses, is it a binomial, trinomial, or are}\hfill & & & \\ \text{there more than three terms?}\hfill & & & \\ \text{It is a trinomial whose coefficient is 1. So undo FOIL.}\hfill & & & 4\left(y\right)\left(y\right)\hfill \\ \text{Use a table like the one below to find two numbers that multiply to}\hfill & & & \\ 14\text{and add to}\mathrm{-9}.\hfill & & & \\ \text{Both factors of 14 must be negative.}\hfill & & & 4\left(y-2\right)\left(y-7\right)\hfill \end{array}$

Check.

$4\left(y-2\right)\left(y-7\right)$

$4(y^2-7y-2y+14)$

$4(y^2-9y+14)$

$4y^2-36y+42✓$