[tex]<b>HEY THERE !![/tex]
Step-1 : Multiply the coefficient of the first term by the constant 12×( -35) = -420
Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is -1 .
-420 + 1 = -419
-210 + 2 = -208
-140 + 3 = -137
-105 + 4 = -101
-84 + 5 = -79
-70 + 6 = -64
-60 + 7 = -53
-42 + 10 = -32
-35 + 12 = -23
. -30 + 14 = -16
-28 + 15 = -13
-21 + 20 = -1
That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 20
12x2 - 21x + 20x - 35
Step-4 : Add up the first 2 terms, pulling out like factors :
3x × (4x-7). Add up the last 2 terms, pulling out common factors :
5 × (4x-7)
Step-5 : Add up the four terms of step 4 :
(3x+5) × (4x-7).
Which is the desired factorization
Final result : (4x - 7) × (3x + 5)
SO YOUR ANSWER IS D.(4x - 7) • (3x + 5)
HOPE IT HELPED YOU.
