How do you factor the trinomial $t^{2} + 13 t + 40$ $t^2 + 13t + 40$ ?

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Answer 1 · 2016-01-16T12:09:46

$(t + 5) (t + 8)$ $color(blue)((t+5))color(brown)((t+8))$

Notice that $5 \times 8 = 40$ $5xx8=40$ and that $5 + 8 = 13$ $5+8=13$

So we have:

$(t + 5) (t + 8)$ $color(blue)((t+5))color(brown)((t+8))$

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$Check by multiplying out the brackets$ $color(blue)("Check by multiplying out the brackets")$

$t (t + 8) + 5 (t + 8)$ $color(blue)(tcolor(brown)((t+8))+5color(brown)((t+8))$

$t^{2} + 8 t + 5 t + 40$ $t^2+8t+5t+40$

$t^{2} + 13 t + 40$ $t^2+13t+40$ This works so the solution is correct!

How do you factor the trinomial t2+13t+40 t^2 + 13t + 40?