SOLUTION: The highest common factor of three polynomials 12x^2+16xy+5y^2, 30x^2-11xy-30y^2 and 6x^2-xy-5y^2 is? Show solution step by step

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: The highest common factor of three polynomials 12x^2+16xy+5y^2, 30x^2-11xy-30y^2 and 6x^2-xy-5y^2 is? Show solution step by step      Log On


   

Question 1133672: The highest common factor of three polynomials 12x^2+16xy+5y^2, 30x^2-11xy-30y^2 and 6x^2-xy-5y^2 is? Show solution step by step
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

To find the greatest common factor (GCF) between numbers, take each number and write its prime factorization. Then, identify the factors common to each number and multiply those common factors together. Bam! The GCF!

+12x%5E2%2B16xy%2B5y%5E2
=+12x%5E2%2B6xy%2B10xy%2B5y%5E2
=+%2812x%5E2%2B6xy%29%2B%2810xy%2B5y%5E2%29
=+6x%282x%2By%29%2B5y%282x%2By%29
=%282+x+%2B+y%29+%286+x+%2B+5+y%29


30x%5E2-11xy-30y%5E2
=30x%5E2-36xy%2B25xy-30y%5E2
=%2830x%5E2%2B25xy%29-%2836xy%2B30y%5E2%29
=5x%286x%2B5y%29-6y%286x%2B5y%29
=%286+x+%2B+5+y%29+%285+x+-+6+y%29


+6x%5E2-xy-5y%5E2
=+6x%5E2-6xy%2B5xy-5y%5E2
=+%286x%5E2-6xy%29%2B%285xy-5y%5E2%29
=+6x%28x-y%29%2B5y%28x-y%29
=%286+x+%2B+5+y%29+%28x+-+y%29

=>The GCF is %286+x+%2B+5+y%29