Question

(ii) 6a2- 31a +35 by 2a-7. divide ​

Answer 1

See Attachment. ︎︎︎︎︎

Answer 2

Factoring 6a2-31a+35

The first term is, 6a2 its coefficient is 6 .

The middle term is, -31a its coefficient is -31 .

The last term, "the constant", is +35

Step-1 : Multiply the coefficient of the first term by the constant 6 • 35 = 210

Step-2 : Find two factors of 210 whose sum equals the coefficient of the middle term, which is -31 .

-210 + -1 = -211

-105 + -2 = -107

-70 + -3 = -73

-42 + -5 = -47

-35 + -6 = -41

-30 + -7 = -37

-21 + -10 = -31 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and -10

6a2 - 21a - 10a - 35

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

3a • (2a-7)

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

5 • (2a-7)

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

(3a-5) • (2a-7)

Which is the desired factorization

Final result :

(2a - 7) • (3a - 5)