Answer:
3k2-13k-56
Final result :
(k - 7) • (3k + 8)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(3k2 - 13k) - 56
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 3k2-13k-56
The first term is, 3k2 its coefficient is 3 .
The middle term is, -13k its coefficient is -13 .
The last term, "the constant", is -56
Step-1 : Multiply the coefficient of the first term by the constant 3 • -56 = -168
Step-2 : Find two factors of -168 whose sum equals the coefficient of the middle term, which is -13 .
-168 + 1 = -167
-84 + 2 = -82
-56 + 3 = -53
-42 + 4 = -38
-28 + 6 = -22
-24 + 7 = -17
-21 + 8 = -13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 8
3k2 - 21k + 8k - 56
Step-4 : Add up the first 2 terms, pulling out like factors :
3k • (k-7)
Add up the last 2 terms, pulling out common factors :
8 • (k-7)
Step-5 : Add up the four terms of step 4 :
(3k+8) • (k-7)
Which is the desired factorization
Final result :
(k - 7) • (3k + 8)
