Question

factorise using middle term splitting
(a) v^2-10v-24​

Answer 1

Factoring v2-10v-24

The first term is, v2 its coefficient is 1 .
The middle term is, -10v its coefficient is -10 .
The last term, "the constant", is -24

Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24

Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -10 .

-24 + 1 = -23
-12 + 2 = -10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 2
v2 - 12v + 2v - 24

Step-4 : Add up the first 2 terms, pulling out like factors :
v • (v-12)
Add up the last 2 terms, pulling out common factors :
2 • (v-12)
Step-5 : Add up the four terms of step 4 :
(v+2) • (v-12)
Which is the desired factorization

Final result :
(v + 2) • (v - 12)

Answer 2

Answer:

Solving

v² - 10v - 24

1.-24= -24

-24 + 1 = -23

-12 + 2 = -10

Now,

v² - 12v + 2v -24

v - (v-12)

2-(v - 12)

$\bold{\red{=> (v+2).(v-12) }}$