Answer:
24w−21
Step-by-step explanation:
Factoring 24w2+10w-21
The first term is, 24w2 its coefficient is 24 .
The middle term is, +10w its coefficient is 10 .
The last term, "the constant", is -21
Step-1 : Multiply the coefficient of the first term by the constant 24 • -21 = -504
Step-2 : Find two factors of -504 whose sum equals the coefficient of the middle term, which is 10 .
-504 + 1 = -503
-252 + 2 = -250
-168 + 3 = -165
-126 + 4 = -122
-84 + 6 = -78
-72 + 7 = -65
-63 + 8 = -55
-56 + 9 = -47
-42 + 12 = -30
-36 + 14 = -22
-28 + 18 = -10
-24 + 21 = -3
-21 + 24 = 3
-18 + 28 = 10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -18 and 28
24w2 - 18w + 28w - 21
Step-4 : Add up the first 2 terms, pulling out like factors :
6w • (4w-3)
Add up the last 2 terms, pulling out common factors :
7 • (4w-3)
Step-5 : Add up the four terms of step 4 :
(6w+7) • (4w-3)
Which is the desired factorization
