How do you factor the expression 3d {}^(2) + 23d + 14 ?

Question

How do you factor the expression

`3d {}^(2) + 23d + 14`
?

Answer 1

`3 {d}^(2) + 23d + 14`

first multiply 14•3 = 42

find 2 numbers that when multiplied it equals to 42 and when added it equals to 23, in this case the numbers are 21 & 2

replace the 23d with the 2 numbers

`3 {d}^(2) + 21d + 2d + 14`
factor out 3d from the expression

`3d(d + 7) + 2d + 14`
then factor out 2 from the expression

`3d(d + 7) + 2(d + 7)`
factor out (d+7)

`(3d + 2)(d + 7)`