How do you factor $2x^2+15x+18$ ?

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Answer 1 · 2016-06-16T10:34:46

$(2x+3)(x+6)$

$2x^2+15x+18 = 2x^2+12x+3x+18 = 2x(x+6)+3(x+6)=(2x+3)(x+6)$ [Ans]

Answer 2 · 2016-06-16T10:57:10

$color(magenta)2x^2 + 15x color(lime)+ color(purple)18$

Find factors of $2 and 18$ which ADD (because of $color(lime)(+)$ 18) to make $15.$

The signs will be the same (because of the $color(lime)(+)18)$ , they are both positive (because of the +15).

$2" "18$
$darr" "darr$

$color(red)(2)" "color(blue)(3) " cross multiply and ADD the products"$
$color(blue)(1)" "color(red)(6)$

$color(red)(2)" "color(blue)(3rArr 1 xx3 = 3)$
$color(blue)(1)" "color(red)(6 rArr 2 xx6 = ul12$
$color(white)(xxxxxxxx.xxxxx)15$

The top line gives one of the factors and the bottom line gives the other factor.

$(2x +3)(x + 6)$

Answer 3 · 2016-06-16T15:38:47

$(2x + 3)(x + 6)$

Use the new AC method (Socratic Search)

$y = 2x^2 + 15 x + 18 = 2(x + p)(x + q)$

Converted trinomial: $y' = x^2 + 15x + 36 = (x + p')(x + q').$

Find $p' and q'$ knowing sum $(b = 15)$ and product $(ac = 36).$

They are: $p' = 3 and q' = 12.$
Back to original $y rarr p = (p')/a = 3/2$ , and $q = (q')/a = 12/2 = 6$ .

Factored form: $2(x + 3/2)(x + 6) = (2x + 3)(x + 6)$

How do you factor 2x^2+15x+182x^2+15x+18?