Question

How do you factor the expression ormula1" title="3d {}^{2} + 23d + 14" alt="3d {}^{2} + 23d + 14" align="absmiddle" class="latex-formula">
?

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)
$(3d + 2)(d + 7)$