Question

Solve - x-13x+42=0
4​

Answer 1

Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, +13x its coefficient is 13 .

The last term, "the constant", is +42

Step-1 : Multiply the coefficient of the first term by the constant 1 • 42 = 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

x2 + 6x + 7x + 42

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+6)

Add up the last 2 terms, pulling out common factors :

7 • (x+6)

Step-5 : Add up the four terms of step 4 :

(x+7) • (x+6)

Which is the desired factorization

Equation