Answer:
(x+3)(2x+7)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(2x2 + 13x) + 21
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+13x+21
The first term is, 2x2 its coefficient is 2 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 2 • 21 = 42
Step-2 : Find two factors of 42 whose sum equals the coefficient of the middle term, which is 13 .
-42 + -1 = -43
-21 + -2 = -23
-14 + -3 = -17
-7 + -6 = -13
-6 + -7 = -13
-3 + -14 = -17
-2 + -21 = -23
-1 + -42 = -43
1 + 42 = 43
2 + 21 = 23
3 + 14 = 17
6 + 7 = 13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 7
2x2 + 6x + 7x + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x+3)
Add up the last 2 terms, pulling out common factors :
7 • (x+3)
Step-5 : Add up the four terms of step 4 :
(2x+7) • (x+3)
Which is the desired factorization
Final result :
(x + 3) • (2x + 7)
- If you want this explained differently please let me know. Hope this helps!
