How do you factor $5x^2+27x+36$ ?

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Answer 1 · 2016-08-14T13:03:41

$(5x+12)(x+3)$

Read all the clues and information from the signs and numbers.

$color(green)(5)x^2color(blue)(+)color(magenta)(27)xcolor(red)+color(green)(36)$

Find factors of $color(green)(5 and 36 )$ which $color(red)(ADD )$ to give $color(magenta)( 27).$

The signs are $color(red)("the SAME")$ , they are $color(blue)"both positive"$

Choose factors and find the cross-products.
A bit of trial and error will result in the following.

$color(white)(.......) 5" "12 rArr 1xx 12 = 12$
$color(white)(.......) 1" "3 rArr 5 xx3 + 15" "12+15 = 27$

The top row is the first bracket, the second row is the second row.

$(5x+12)(x+3)$

How do you factor 5x^2+27x+365x^2+27x+36?