Is there any easier way used to split the middle term? Is there any easier way for the calculation?
Is there any easier way used to split the middle term? Is there any easier way for the calculation?
As we know for factorizing a quadratic polynomial, we may also use a method “ By splitting the middle term” , which sometimes becomes slightly difficult if you are not able to split the middle term. You may possibly follow the following easy way out… Like, example: factorize 46x² + 43x - 39 =0
As you know , to start with, we try to get 2 numbers into which the middile term is to be split. The sum of these numbers should be +43 & the product should be (46x -39) = -1794.
Since here the product is -ve , so one number should be +ve & one should be -ve. Greater one should be +ve as the middle term is + ve.
Now to get those numbers , we prime factorize 1794. So its prime factors, when we calculate, we get step wise.. 1794 = 2 x897
1794 = 2 x 3 x 299
1794 = 2 x3 13 x 23
So, we may try with all these factors to check the Sum . The sum should be +43. So, we try 2 & 897. Ans is no. Then take 2,3 & 299 ie 6 & 299. Again ans is no. Then take 2,3,13 & 23. & try to guess, Yesss!!! We got, 2 x13 And 3x23 . That is, 26 & 69 . So those numbers are -26 & +69 & their sum is + 43..
Then once you split the middle term into 2. You may proceed with your process…
Like, example: factorize 46x² + 43x - 39 =0
As you know , to start with, we try to get 2 numbers into which the middile term is to be split. The sum of these numbers should be +43 & the product should be (46x -39) = -1794.
Since here the product is -ve , so one number should be +ve & one should be -ve. Greater one should be +ve as the middle term is + ve.
Now to get those numbers , we prime factorize 1794. So its prime factors, when we calculate, we get step wise.. 1794 = 2 x897
1794 = 2 x 3 x 299
1794 = 2 x3 13 x 23
So, we may try with all these factors to check the Sum . The sum should be +43. So, we try 2 & 897. Ans is no. Then take 2,3 & 299 ie 6 & 299. Again ans is no. Then take 2,3,13 & 23. & try to guess, Yesss!!! We got, 2 x13 And 3x23 . That is, 26 & 69 . So those numbers are -26 & +69 & their sum is + 43..
Then once you split the middle term into 2. You may proceed with your process…
