Question

solve the following quadratic equation by the factorization 4root 6x^2-13x-2root6=0​

Answer 1

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