SOLUTION: Please help me solve this problem.... REWRITE THE MIDDLE TERM AS THE SUM OF TWO TERMS AND THEN FACTOR COMPLETELY. 12w^2+19w+4

Question 44877: Please help me solve this problem....
REWRITE THE MIDDLE TERM AS THE SUM OF TWO TERMS AND THEN FACTOR COMPLETELY.
12w^2+19w+4
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
It is not the "MIDDLE TERM"; it is "COEFFICIENT OF THE MIDDLE TERM".

Here,
COEFFICIENT OF THE FIRST TERM (i.e. coefficient of ) = 12,
COEFFICIENT OF THE MIDDLE TERM (i.e. coefficient of ) = 19,
COEFFICIENT OF THE LAST TERM (i.e. coefficient of ) = 4.

To solve this type of problems, follow the following steps.

1. Find the product of the coefficients of the first and last terms (here, 12 x 4 = 48).
2. Express this product (here, 48) into two factors such that the sum of these factors is equal to the coefficient of the middle term. Here such factors are 16 and 3. Note: 16 x 3 = 48 and 16 + 3 = 19.
3. Then re-write the expression (here, ).
4. Take the common terms in brackets (here, ).
5. Re-write the expression (here, ). Thus you get the factors required.

In this case the factors are (3w + 4) and (4w + 1).
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