SOLUTION: Could someone explain to me exactly how to work these problems. It is like another language to me. Rewrite the middle term as the sum of two terms and the factor completely.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Could someone explain to me exactly how to work these problems. It is like another language to me. Rewrite the middle term as the sum of two terms and the factor completely.       Log On


   

Question 88853: Could someone explain to me exactly how to work these problems. It is like another language to me.
Rewrite the middle term as the sum of two terms and the factor completely.
A)12w^2+19w+4
B)4z^3-18z^2-10z
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.