solve the following quadratic equation by the factorization 4root 6x^2-13x-2root6=0
Answers
Factoring 6x2+13x+6
The first term is, 6x2 its coefficient is 6 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 6 • 6 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 13 .
-36 + -1 = -37
-18 + -2 = -20
-12 + -3 = -15
-9 + -4 = -13
-6 + -6 = -12
-4 + -9 = -13
-3 + -12 = -15
-2 + -18 = -20
-1 + -36 = -37
1 + 36 = 37
2 + 18 = 20
3 + 12 = 15
4 + 9 = 13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 9
6x2 + 4x + 9x + 6
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 :
3 • (3x+2)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (3x+2)
Which is the desired factorization