What is the simplest way to do mid term splitting for larger digit no. Like x^2+2x-195 plzz explain via more examples.
What is the simplest way to do mid term splitting for larger digit no. Like x^2+2x-195 plzz explain via more examples.
Factoring x2-2x-195
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -195
Step-1 : Multiply the coefficient of the first term by the constant 1 * -195 = -195
Step-2 : Find two factors of -195 whose sum equals the coefficient of the middle term, which is -2 .
-195 + 1 = -194 -65 + 3 = -62 -39 + 5 = -34 -15 + 13 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 13
x2 - 15x + 13x - 195
Step-4 : Add up the first 2 terms, pulling out like factors :
x * (x-15)
Add up the last 2 terms, pulling out common factors :
13 * (x-15)
Step-5 : Add up the four terms of step 4 :
(x+13) * (x-15)
Which is the desired factorization
Factoring x2-2x-195
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -195
Step-1 : Multiply the coefficient of the first term by the constant 1 * -195 = -195
Step-2 : Find two factors of -195 whose sum equals the coefficient of the middle term, which is -2 .
| -195 | + | 1 | = | -194 | ||
| -65 | + | 3 | = | -62 | ||
| -39 | + | 5 | = | -34 | ||
| -15 | + | 13 | = | -2 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 13
x2 - 15x + 13x - 195
Step-4 : Add up the first 2 terms, pulling out like factors :
x * (x-15)
Add up the last 2 terms, pulling out common factors :
13 * (x-15)
Step-5 : Add up the four terms of step 4 :
(x+13) * (x-15)
Which is the desired factorization
