Online Algebra 1 Practice Tutors - Algebra 1 Tutors

Online Algebra 1 Practice Tutors - Algebra 1 Tutors H.C.F. (Highest common factor) and L.C.M. (Lowest common factor) is the part of algebra 1. Methods to solve H.C.F and L.C.M.: - Division method Factorization method. Lets practice few problems of algebra 1:- Example: - Find out the L.C.M. and H.C.F. by factorization i) X^2 + x, x^3 x ii) X^3 + 2 x^2, x^3 + 3 x^2 + 2 x Solution: - i) 1st expression = x^2 + x = x ( x + 1) 2nd expression = x^3 x = x ( x^2 -1) = x (x + 1) (x 1) The common factors of the two expressions are x and (x +1). Therefore H.C.F. = x (x + 1) (x 1) is the extra factor in the 2nd expression. Hence the required L.C.M. = x (x + 1) (x 1) ii) 1st expression = x^3 + 2 x^2= x^2 (x + 2) = x * x * ( x +2) 2nd expression = x^3 + 3 x^2 + 2 x = x(x^2+3x+ 2)=x (x^2 + 2 x + x + 2) =x {x ( x + 2 ) + 1 ( x + 2 )} =x (x + 2) (x + 1) In both the expressions, the common factors are x and x + 2 Therefor H.C.F. = x (x + 2) The extra factors are x in the 1st expression and x + 1 in the 2nd expression. Therefore L.C.M. = x ( x + 2) x (x + 1) = x^2 (x+1)(x+2)