Question 88853
Rewrite the middle term as the sum of two terms and the factor completely. 
A)12w^2+19w+4
Think of two numbers whose product is 4*12=48 
and whose sum is 19
The numbers are 3 and 16
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Rewrite 19w as 3w+16w to get:
12w^2+3w+16w+4
Factor the 1st two and the last two terms separately:
3w(4w+1)+ 4(4w+1)
Factor again to get:
(4w+1)(3w+4)
Comment: This is called the AC Method of factoring trinomials.
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B)4z^3-18z^2-10z
z(4z^2-18z-10)
Think of two numbers whose product is -10*4=-40
and whose sum is -18
The numbers are -20 and +2
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Replace -18z by -20z+2z to get:
z(4z^2-20z+2z-10)
= z(4z(z-5)+2(z-5))
= z(z-5)(4z+2)
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Cheers,
Stan H.