How do you factor $y=(5x+2)^2 + 11(5x+2)+30$ ?

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Answer 1 · 2016-01-18T10:45:44

$color(green)(y=(5x+7)(5x+8))$

Have a look at the 'trick' I used!

Multiply out the brackets so that you can collect like terms and simplify:

Let $(5x+2)$ be z then we have

$y=z^2+11z+30$

Factors of 30 are: {1,30} ; {2, 15} ; {3,10} ; {5,6}

We observe that 5+6=11 so we try those first:

$y=(z+5)(z+6) =z^2+6z+5z+30 color(red)(" This works")$

Substitute back for z giving:

$y=[(5x+2)+5)([5x+2]+6)$

$color(green)(y=(5x+7)(5x+8))$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check by multiplying out the brackets

$y=(5x+7)(5x+8)$

$y= 25x^2+40x+35x+56color(white)(...) = 25x^2+75x+56 color(red)(" This works")$

How do you factor y=(5x+2)^2 + 11(5x+2)+30 y=(5x+2)^2 + 11(5x+2)+30 ?