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A new synthesis technique for the linear phased array is developed based on using the array polynomial technique. The array factor is expressed as the product of subpolynomials such that their roots are located on the unit circle. All array elements are active for any arbitrary non-prime number of the array elements. Null steering for interference suppression is obtained by using one subploynomial to steer only one null. The results show that the developed method in the form of an analytical solution can synthesize the prescribed patterns and exact null locations using the phase shifters of the linear arrays.