Factorization by Middle Term Splitting
Factorization by Middle Term Splitting
Factorization of quadratic polynomials in one Variables:
Let us now consider the polynomial .
Comparing 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 ab is positive. Therefore, a and b both must negative
Clearly, such factors 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.
Illustration: Factorize the following expression:
Solution: In order to factorize , we find two numbers p and q such that
p + q + 6 and pq = 8
Clearly, 2 + 4 = 6 and 2 4 = 8.
We now split the middle term 6x in the given quadratic as 2x + 4x.
The sum and the difference of two expressions are | |||
| Right Option : D | |||
| View Explanation | |||
Factorize: | |||
| Right Option : B | |||
| View Explanation | |||
Solve | |||
| Right Option : A | |||
| View Explanation | |||
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