How do you write #d^2+12d+32# in factored form?

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Answer 1 · 2015-09-17T17:01:58

#color(blue)((d+4)(d+8)# is the factorised form of the expression.

#d^2+12d+32#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ad^2 + bd + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*32 = 32#
and
#N_1 +N_2 = b = 12#

After trying out a few numbers we get #N_1 = 8# and #N_2 =4#
#8*4 = 32#, and #8+4= 12#

#d^2+12d+32 = d^2+8d +4d+32#

#d(d+8) +4(d+8)#

#color(blue)((d+4)(d+8)# is the factorised form of the expression.

Answer 2 · 2015-09-17T18:48:25

Factor: #d^2 + 12d + 32#

Ans: #(x + 4)(x + 8)#

I use the new AC Method (Socratic Search)

#y = d^2 + 12d + 32 = (d + p)(d + q)#

Factor pairs of #(32) -> (2, 16)(4, 8)#. This sum is

#4 + 8 = 12 = b#

Then #p = 4# and #q = 8#

Factored form: #y = (d + 4)(d + 8)#

NOTE . This new AC Method shows a systematic way to find the 2 numbers p and q. It also avoids the lengthy factoring by grouping.