6x square +19x +10 ÷ 2x +5
Answers
6x²+19x+10÷2x+5
Solution:
Trying to factor by splitting the middle term
2.1 Factoring 6x2 + 19x + 10
The first term is, 6x2 its coefficient is 6 .
The middle term is, +19x its coefficient is 19 .
The last term, "the constant", is +10
Step-1 : Multiply the coefficient of the first term by the constant 6 • 10 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is 19 .
-60 + -1 = -61
-30 + -2 = -32
-20 + -3 = -23
-15 + -4 = -19
-12 + -5 = -17
-10 + -6 = -16
-6 + -10 = -16
-5 + -12 = -17
-4 + -15 = -19
-3 + -20 = -23
-2 + -30 = -32
-1 + -60 = -61
1 + 60 = 61
2 + 30 = 32
3 + 20 = 23
4 + 15 = 19 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 15
6x2 + 4x + 15x + 10
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (3x+2)
Add up the last 2 terms, pulling out common factors :
5 • (3x+2)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (3x+2)
Which is the desired factorization
Canceling Out :
2.2 Cancel out (2x+5) which appears on both sides of the fraction line.
Final result :
3x + 2