Question

Simplify: 12(y² + 7y + 10) ÷ 6(y + 5)​

Answer 1

1.1 Factoring y2 + 7y + 10

The first term is, y2 its coefficient is 1 .

The middle term is, +7y its coefficient is 7 .

The last term, "the constant", is +10

Step-1 : Multiply the coefficient of the first term by the constant 1 • 10 = 10

Step-2 : Find two factors of 10 whose sum equals the coefficient of the middle term, which is 7 .

-10 + -1 = -11

-5 + -2 = -7

-2 + -5 = -7

-1 + -10 = -11

1 + 10 = 11

2 + 5 = 7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 5

y2 + 2y + 5y + 10

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

y • (y+2)

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

5 • (y+2)

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

(y+5) • (y+2)

Which is the desired factorization

Equation at the end of step

1

:

(y + 5) • (y + 2)

12 • —————————————————

6y + 5

STEP

2

:

Final result :

12 • (y + 5) • (y + 2)

——————————————————————

6y + 5