How do you factor the trinomial #r^2 + 15r + 54 = 0#?

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Answer 1 · 2018-05-30T17:17:39

#(r+6)(r+9)#

#"the factors of + 54 which sum to + 15 are + 6 and + 9"#

#r^2+15r+54=(r+6)(r+9)#

Answer 2 · 2018-05-30T17:20:30

#r^2 + 15r + 54 = (x+6)(x+9)#

#r^2 + 15r + 54#

find two number that have a product of 54 and a sum of 15:

1 + 14
2 + 13
3 + 12
4 + 11
5 + 10
6 + 9 works!

Factors are:

#(x+6)(x+9)#

#x=-6# and #x=-9# as this graph of the function shows:

graph{x^2 + 15x + 54 [-16.59, 3.41, -4.4, 5.6]}