Factorization by Middle Term Splitting
Factorization by Middle Term Splitting
Factorization by Middle Term Splitting:
Factorization of quadratic ploynomials in one Variables:
Let us now consider the polynomial .
Compairing this with polynomial , we get a + b = -7 and ab = 12.
Now, we have to find factors of 12 whose sum is -7.
Since a + b is negative abd ab is positive. Therefore, a and b both must negative
Clearly, such factos are -3 and -4.
Hence, the factors of are (y - 3) and ( y - 4 ).
Algorithm:
Step I Obtain the quadratic polynomial .
Step II Obtain p = coefficient of x and, q = constant term.
Step III Find two numbers a and b such that a + b = p and ab = q.
Step IV Split up the middle term as the sum of two terms ax and bx.
Step V Factorize the expression obtained in step IV by grouping the terms.
Example: Factorize each of the following expressions:
Solution (i) In order to factorize , we find two numbers p and q such that
p + q + 6 and pq = 8
Clealry, 2 + 4 = 6 and 2 4 = 8.
We now split the middle term 6x in the given quadratic as 2x + 4x.
(ii) In order to factorize , we have to find two numbers p and q such that
p + q = 4 and pq = -21
Clearly, 7 + (-3) = 4 and 7 -3 = -21
We now split the middle term 4x of as 7x - 3x
(iii) In order to factorize we have to find two numbers p and q such that
p + q = -7 and pq = 10
Clearly, - 5- 2 = -7 and -5 -2 = 10
We now split the middle term -7x of the given quadratic as -2x - 5x
Express the following as the product of two factors: | |||
| Right Option : C | |||
| View Explanation | |||
One of the factor of the polynomial | |||
| Right Option : B | |||
| View Explanation | |||
Factorize: | |||
| Right Option : D | |||
| View Explanation | |||
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