Determine whether the statement makes sense or does not make sense, and explain your reasoning. Although 20x3 appears in both 20x3+8x2 and 20x3+10x ,I’ll need to factor 20x3 in different ways to obtain each polynomial’s factorization.

Question

Determine whether the statement makes sense or does not make sense, and explain your reasoning.  Although 20x3 appears in both 20x3+8x2 and 20x3+10x ,I’ll need to factor 20x3 in different ways to obtain each polynomial’s factorization.

Paul Mitchell · Accepted Answer

Step 1  Given:  20x3+8x2 and 20x3+10x  Step 2  Yes! statement makes sense  20x3+8x2  Break terms:  =2x×2x×5x+2x×2x×2  Take common out:  =2x×2x(5x+2)  =4x2(5x+2)  Step 3  20x3+10x  Take common out:  =10x(2x2+1)

SlabydouluS62 · Accepted Answer

The statement  makes sense because the two polynomials each contain another term which has a different common factor with 20x3

Vasquez · Accepted Answer

The statement makes sense because polynomials have a different greatest common factors. Hence, 20x3 will be factored differently. In the first polynomial the greatest common factor is 4x2. Hence, we factor it out: 20x3+8x2=4x2(5x+2) In the second polynomial the greatest common factor is 10x so, we factor it out: 20x3+10x=10x(x2+1) Result: It makes sence.