how to find the range of a group of numbers

In many situations, we come across polynomials, which may not have common factors among its terms. In such cases, we group the terms of the expression in such a way that there are common factors among the terms of the groups so formed. Let us study such exampl..

There are various methods of factorising a polynomial. They are, 1. Factorisation by dividing the expression by the HCF of the terms of the given expression. 2. Factorisation by grouping the terms of the expression. 3. Factorisation using identities. Let us study these methods one after ..

Identify the HCF of the terms of the groups. Now, observe that, (2x - 3a) is a common factor for both the groups. Therefore (2x - 3a) is one of the factors of the given expression. The other factor is identified by dividing each group by the common factor i.e. (..

You know that any polynomial of the form p(a) can also be written as p(a) = g(a) x h(a) + R(a) it implies that Dividend = Quotient X Divisor + Remainder. If the remainder is zero, then p(a) = g(a) x h(a). That is, the polynomial p(a) is a product of two other polynomials g(a) and h(a). There ..

Step 1: The factor pairs of the last term are (7,2), (14,1), (-1,-14). Step 2: The pair of factors whose sum is equal to -15, the co- efficient of the middle term is (-1,-14). Step 3: Rewrite the expression using these factors Step 4: Group the terms and factorise. ..

Step 1: The factor pairs of the third term are ((7,4); (14,2); (28, 1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is 14 and 2. Step 3: Rewrite the expression using these factors Step 4: Group the terms and factorise. ..

Step 1: Factor pairs of the last term are (-7,+3), (21,-1), (+7,-3), (-21,+1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (+7,-3). Step3: Rewrite the expression using these factors as w 2 + 7w - 3w -21. Step 4: Group the terms and factorise...

To find the logarithm of a Complex number - Let z= x + iy be a complex number. Taking log on both side..

One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. And z 1/q be the q th root of z. Through De ..

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