PLEASE HELP PLEASE Donna orders boxes of batteries for calculators in the math class she teaches. She knows that
the number of batteries she gets, n, is proportional to how many boxes, b, of batteries she
buys. In previous years she has recorded what is shown in the table. What is the ratio of the
number of batteries to the number of boxes? What does it represent?
Number of boxes , b 11, 15, 21. Number of batteries, n 44, 60, 84

When factored completely, is equivalent to

To factorize the polynomial

notice that the GCF of each term is m. So we can factorize m out of each term as follows

the fourth-degree polynomial in the brackets an be treated as a quadratic polynomial

and factorized as such. The quadratic has the constant term . We have to look for factors of that add up to  (the co-efficient of the term).

The factors that satisfy the condition are and . So we can factorize the fourth-degree polynomial as

We have factorized the polynomial so far as

But the factor is a difference of two squares and can be factorized as

Our final factored polynomial is

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